ABSTRACT. We provide a robust (or detail-free) strategic foundation for the Walrasian Equilibrium: a mechanism for an exchange economy with asymmetric information and interdependent values that is ex-post individually rational, incentive compatible, generates budget surplus and is ex-post nearly Pareto Efficient, when there are many agents. The level of inefficiency is proportional to the impact a single agent has on the Walrasian price. Conversely, we show that mechanisms generating smaller efficiency losses must violate some of the constraints, and so our efficiency bound is tight. The tight robust asymptotic efficiency is achieved by σ-Walrasian Equilibrium mechanisms, in which the allocation is as if each agent traded knowing all the information distributed in the economy, faced with the price that increases in the quantity traded with slope σ.

ABSTRACT. We consider a multi-object private values setting with quantity externalities: a value to a bidder from an object may depend on the total number of objects sold. For example, the likelihood a customer will respond to an advertisement is higher the fewer other advertisements are shown; a spectrum license is more valuable the fewer licenses are being allocated. We raise and solve the problem of finding revenue maximizing and efficiently allocating auctions in such a setting. We show that both optimal and efficient auctions have the property that the quantity of objects sold depends non-trivially on the whole profile of players' valuations. That is, the quantity to sell is determined endogenously, within the auction. We demonstrate that auctions currently used for allocating advertising positions are suboptimal and offer simple designs that can implement (or approximate) optimal and efficient auctions under quantity externalities.

ABSTRACT. We consider a pricing problem where a buyer is interested in purchasing/using a good, such as an app or music, repeatedly over time. The consumer's value for the good evolves with each use. Optimizing seller's revenue in such dynamic settings is a complex problem and requires assumptions about buyer's behavior before learning his future value(s), and in particular, how he reacts to risk.

We ask whether it is possible to achieve meaningful revenue guarantees in such a setting in a detail-free manner. We explore the performance of a class of simple-to-use pricing mechanisms where the buyer reacts to prices myopically and the seller needs to optimize for revenue over a space of only two parameters. We show that when the buyer's value evolves as a martingale, a pricing mechanism of this form is approximately optimal regardless of the buyer's risk profile or fine details of the value evolution process.

ABSTRACT. We investigate the bids submitted in spectrum auctions conducted by the Federal Communications Commission (FCC) during 1994-2008, most of which were simultaneous ascending auctions. Jump bidding was prevalent in these auctions. We test whether complementarity and substitutability among the auctioned licenses, the degree of competition, and the imposed rules affect bidders' jump-bidding behavior. We also test whether jump bidders were successful in deterring competitors and paying less when they win.

ABSTRACT. We study a partnership model with non-identical type distributions and interdependent values. For any convex combination of revenue and social surplus in the objective function, we derive the optimal dissolution mechanism for arbitrary initial ownership. This mechanism involves ironing around worst-off types, which are endogenously determined and typically interior. Given the optimal mechanism, we then determine the optimal initial ownership structures. Equal ownership is always optimal with identical distributions but not with non-identical distributions. When distributions are ranked by stochastic dominance, stronger agents receive higher initial ownership shares when the weight on revenue is small but not necessarily when it is large.

ABSTRACT. We analyze the economic impact of process innovations when the innovator sells licenses to both potential entrants and incumbent firms. Licenses are sold by auction aiming to maximize the revenue of the innovator. The post innovation market structure, the diffusion of the innovation and the incentive to innovate are compared with the case where licenses are sold only to incumbent firms and not to entrants. It is shown, quite surprisingly, that opening the market to entrant licensees, the incentive to innovate is maximized in a monopoly market rather than oligopoly or competitive markets and this is true for drastic as well as non-drastic innovation.

ABSTRACT. We analyze a credence goods market with regulated prices and heterogeneous experts. Experts are assumed to differ in the cost of treating a minor problem. We investigate the effect of this heterogeneity on the market level of fraud and overall welfare. We show that a cost reduction does not always increase welfare. We also analyze the incentives to invest in a cost reduction and find that a cost reduction increases welfare if sufficiently many experts are affected by it.

ABSTRACT. We theoretically and experimentally examine three common market institutions. In “posting”, sellers post fixed prices that are seen by buyers who then choose which seller to visit. Under “haggling”, prices are not posted, but emerge via negotiation or bidding depending on how many potential trading partners a seller has. Under “flexible pricing”, prices are posted but can be negotiated upwards or downwards like under haggling. We find that efficiency is highest under posting, though differences become smaller with time and experience. Transaction prices and thus sellers’ surplus are highest under haggling and lowest under posting, while buyers’ surplus has the reverse ordering. When there is local excess demand, sellers appropriate a majority of the surplus, but substantially less than the predicted amount. When there is no local excess demand, bargaining tends to favour the seller relative to the predictions of standard bargaining theory.

ABSTRACT. A principal can hire an agent of hidden ability, but strictly prefers his outside option to hiring a low type. The agent's output when working is not observable so they cannot contract on performance. Every period that the agent is hired, a simultaneous move game is played. The principal sets the agent a test which is costless for the high type to pass and costly for the low type to pass, and the principal can monitor the result of the test at a cost. Without commitment, the principal's payo in equilibrium is the same as never monitoring, independent of the cost of monitoring. With commitment, the principal's optimal contract involves monitoring even after learning that the agent is the high type.

ABSTRACT. We consider the problem of sequential search with free recall and discounting. Performance of a search rule for a given prior is measured as the fraction of the maximal payoff under this prior. A search rule is robust if it has a high performance under every prior. Bayesian search rules are not robust as, while being optimal under one prior, they can perform very poorly under a different prior. We present a search rule that performs well after any search history under any prior with a given support. In each round the rule stops searching with a probability that is linear in the best previous offer.

ABSTRACT. We present a partnership model where heterogeneous agents bargain over the gains from trade and search on the match. Frictions allow agents to extract higher rents from more productive partners, generating an endogenous preference for high types. More productive agents upgrade their partners faster, therefore the equilibrium match distribution features positive assortative matching. Frictions are commonly understood to hamper sorting. Instead, we show how frictions generate positive sorting even with a submodular production function. Our results challenge the interpretation of positive assortative matching as evidence of complementarity.

ABSTRACT. This paper analyzes double-auction two-player bargaining with private values. We consider a setting with discrete two-value overlapping distributions of traders' valuations. We characterize all pure-strategy equilibria in the presence of traders that behave naively, i.e. set bid or ask equal to their valuation or cost. We show theoretically that equilibrium efficiency can be lower with more such traders. In the experiment, we vary the proportion of naive traders by introducing the possibility of being matched with a computer who behaves in the naive manner. Despite the theoretical possibility, efficiency is not lower with more naive traders in the experiment. Subjects behave strategically, setting bids lower than their values and asks higher than their costs, but they do not realize that the presence of more naive players allows for more strategic behavior. We also find evidence that framing the double auction as a direct mechanism lead to more naive behavior.

ABSTRACT. Most negotiations involve risks that are only revealed ex-post. Often these risks are not incurred equally by the parties involved. We experimentally investigate bargaining situations where one player is exposed to ex-post risk, whereas the other is not. We find that residual claimants extract a risk premium, which increases in risk exposure. This premium is sometimes high enough to make it advantageous to bargain over a risky rather than a risk-less pie. Standard theory captures some of our observations but important issues remain. First, comparatively less risk averse residual claimants benefit the most. Second, when given the chance, residual claimants tend to choose a riskier distribution of surpluses only when there is the possibility of an equal-split ex-post. Third, bargaining frictions increase as risk increases. Our results indicate that bargaining models require separation between the determinants of bargaining power and fair compensation for risk exposure.

ABSTRACT. In this paper we experimentally investigate factors that affect the proposal power in Baron-Ferejohn legislative bargaining experiments. As is shown in the previous literature about experimental bargaining, we find that proposal power is smaller than what the equilibrium model predicts. However, the proposal power of legislators decreases in the extent to which people value the future payoffs (discount factor), increases in the number of bargaining group size (competition effect), and appears greater under simple majority than unanimity rule. Our study thus confirms the comparative static predictions of rational-choice model of multilateral bargaining and suggests simple but important controls for proposer behavior.

ABSTRACT. Many multi-period matching markets exhibit some level of commitment. That is, agents' ability to terminate an existing relationship is somehow restricted by cost of divorce, binding contracts or social norms. Based on real-world examples, this paper models matching markets with commitment of different restrictive power, defines notions of stability and corresponding stable mechanisms, as well as specifying conditions for efficiency, strategy-proofness and other properties. Specifically, the market with full commitment (no divorce) resembles the static matching market the most, but there is no stable matching mechanism based on spot markets without assuming no preference cycle. By comparison, the market with one-sided commitment requires more assumptions about preferences, such as Sequential Improvement Complementarity (SIC, Kadam and Kotowski, 2015a), to produce satisfactory outcomes. We also show how to incorporate external entries and exits of agents, which are incompatible with SIC, into the model with one-sided commitment.

ABSTRACT. In actual school choice applications the theoretical underpinnings of the Boston Mechanism (BM) (complete information and rationality of the agents) are often not given. We analyze the actual behavior of agents in such a matching mechanism, using data from the matching mechanism currently used in a clearinghouse at Paderborn University, where a variant of BM is used and supplement this data with data generated in a survey among students who participated in the clearinghouse. We find that under the current mechanism over 70% of students act strategically. Controlling for students' limited information, we find that they do act rationally in their decision to act strategically. However, we do not find evidence that they follow any of the strategies advised in the literature. While students thus seem to react to the incentives to act strategically under BM, they do not seem to be able to use this to their own advantage.

ABSTRACT. We study many–to–one matching problems where doctors have strict preferences over hospitals, hospitals have strict preferences over sets of doctors, and the law assigns priorities to hospitals over sets of doctors. We are interested in mechanisms that are efficient, stable, strategy-proof, minimize unfilled positions, and respect priorities. We show that the mechanisms used in Colombia do not satisfy any of these properties. We modify three mechanisms: the deferred acceptance, the immediate acceptance, and the top trading cycle. None of these mechanisms is efficient and stable, but all minimize unfilled positions. The deferred acceptance and the top trading cycle are strategy-proof. The deferred acceptance is the only one that respects priorities. We introduce a weakening of stability and efficiency, constrained stability and constrained efficiency respectively. We show that the deferred acceptance is the only constrained stable, but the top trading cycles and the immediate acceptance are the only constrained efficient.

ABSTRACT. We consider the allocation problem of assigning heterogeneous objects to agents and determining their payments. Each agent receives at most one object. Agents have non quasi-linear preferences over pairs consisting of an object and a payment. Under non quasi-linear setting, we focus on the situations where if objects are equally priced, (i) agents have the common ranking over objects or (ii) objects are partitioned into several tiers, and agents have the common ranking over object tiers. The minimum price Walrasian rule is a rule that assigns a minimum price Walrasian equilibrium to each preference profile. We establish that on both common object ranking domain and common tiered object domain, an allocation rule satisfies efficiency, strategy-proofness, individual rationality and no subsidy if and only if it is the minimum price Walrasian rule. Similar characterizations hold for subdomains including preferences only exhibiting positive income effects, or only exhibiting negative income effects.

ABSTRACT. We introduce partial strategyproofness, a relaxed notion of strategyproofness, to study the incentive properties of non-strategyproof assignment mechanisms. Under partially strategyproof mechanisms, truthful reporting is a dominant strategy for agents whose values for any two objects are sufficiently different. A single numerical parameter, the degree of strategyproofness, controls the extent to which agents’ values must differ. We provide a new axiomatic decomposition of strategyproofness, and we show that partial strategyproofness arises by dropping the least important of the axioms and that the underlying domain restriction is maximal. Then we show that partial strategyproofness can alternatively be defined in terms of partial dominance, that it is intermediate between strategyproofness and many relaxed incentive concepts, and that it unifies two prior local sufficiency results. It enables the comparison of important non-strategyproof mechanisms such as Probabilistic Serial, two variants of the Boston mechanism, the HBS Draft mechanism, and new hybrid mechanisms.

ABSTRACT. We consider general allocation problems with indivisibilities where agents' preferences possibly exhibit externalities. In such contexts many different core notions were proposed. One is the gamma-core whereby blocking is only allowed via allocations where the non-blocking agents receive their endowment. We show that if there exists an allocation rule satisfying individual rationality, efficiency, and strategy-proofness, then for any problem for which the gamma-core is non-empty, the allocation rule must choose a gamma-core allocation and all agents are indifferent between all allocations in the gamma-core. We apply our result to housing markets, coalition formation and networks.

ABSTRACT. In this talk, we will describe the use of interior-point methods to find Nash equilibria for discrete-time Markov games with discounting. The approach uses the formulation for the Nash equilibrium conditions for a stationary strategy as a nonlinear complementarity problem, with dual variables representing expected payoffs. We formulate the equations of the central path for a primal-dual interior-point method, and show that these can be efficiently solved using Newton's method, with the dual variable updates determining the updates of the primal variables. We illustrate our approach with an example of a simple two-player game, and consider the limiting solutions without discounting.

ABSTRACT. This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with complete information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general dynamic games with simultaneous moves (i.e. almost perfect information), and (2) the existence of pure-strategy subgame-perfect equilibria in perfect-information dynamic games with uncertainty. Our results go beyond previous works on continuous dynamic games in the sense that public randomization and the continuity requirement on the state variables are not needed. As an illustrative application, a dynamic stochastic oligopoly market with intertemporally dependent payoffs is considered.

ABSTRACT. We introduce the notion of type-symmetric randomized equilibrium (TSRE) by requiring those agents with the same type of characteristics to choose the same randomized choice. Such a notion provides a generic micro-foundation for the macro notion of equilibrium distribution, as used in the literature on games and economies with many agents. In particular, we show that if the space of agents is modeled by the classical Lebesgue unit interval, any Nash (resp. Walrasian) equilibrium distribution in a large game (resp. economy) is uniquely determined by one TSRE. Furthermore, we provide examples to demonstrate that this uniqueness characterization does not necessarily hold when a non-Lebesgue agent space is used.

ABSTRACT. The economist’s ideal of a perfectly competitive market involves many participants. Such a market is often described using a game with many players. Similar games arise when economists discuss public finance, mechanism design, insurance, and macromodels of national or international economies. Formally, the player set in a large game has usually been represented by the uniform probability distribution over the Lebesgue unit interval of the real line. Yet this poses significant measurability issues, especially when considering a probability distribution over profiles of all players’ strategies. This has recently led some mathematical economists to explore greatly enriched player spaces. Here I propose a more workable “statistical” approach that distinguishes between the unit interval of potential players and the countably infinite set of actual players drawn randomly from this interval. Then a suitable Bayesian Nash “statistical” equilibrium in pure strategies exists for a broad class of large games.

ABSTRACT. We consider Nash equilibria of large semi-anonymous finite-player games which are nearly pure, in the sense that a large fraction of players play a pure strategy. We show that (a) nearly-pure Nash equilibria may fail to exist no matter how large the number of players is, (b) regular equilibria of non-atomic games may fail to yield a nearly-pure Nash equilibrium in all sufficiently large finite-player games that are sufficiently close to the non-atomic game and (c) the same holds for strict equilibria of non-atomic games with infinite action spaces. Despite these difficulties, we show that for generic distributions of players' characteristics (i.e. action sets and payoff functions), nearly-pure Nash equilibria exist in all sufficiently large finite-player games with a distribution of characteristics sufficiently close to the given one. This result is then applied to the setting of Mas-Colell (1983).

ABSTRACT. We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a player has an incentive to adopt, that would be "evolutionary stable" or that could "learn itself". Rather, a player can strategically teach such a learning opponent in order secure at least the Stackelberg leader payoff. This hold even when we restrict to the class of generic games, two-player games, potential games, games with strategic complements or 2x2 games, in which learning is known to be "nice". It also applies to uncoupled learning heuristics leading to correlated equilibria, rationalizability, iterated admissibility, or minimal curb sets.

ABSTRACT. We conduct an experimental study on behavior and cognition in various 2×2 games with/without role-switching from the perspective of inductive game theory (IGT). Here, subjects have no prior knowledge about payoffs and can only learn them by playing the game. Without role-switching, subjects can, and many do, successfully learn their own payoffs. To learn the payoffs of the other, role-switching is required. While this gives more information about the whole structure, subjects do not learn all payoffs successfully. We find that role-switching has both behavioral and cognitive effects. On the behavioral side, without role-switching, many subject pairs converged to a Nash equilibrium. With role-switching, subject pairs converged to either Nash or ICE (intrapersonal coordination equilibrium) maximizing the average payoffs, as predicted by IGT. On the cognitive side, correct recall of payoffs is positively correlated with the number of experiences but is negatively correlated with convergence to some action pair.

ABSTRACT. I study a model of strategic experimentation with direct payoff externalities. A continuum of forward-looking players compete for a scarce resource; each player's valuation is uncertain, and evolves independently from other players. The strategic interaction arises from congestion, as players engage in costly queueing in their exploration phases.

I solve for the unique stationary equilibrium under different service disciplines, and address the problem of designing the optimal service discipline. Congestion always generates over-experimentation with respect to the efficient solution. Next, I study the problem of the monopolist who chooses the throughput rate in order to maximize profit. The optimal level of congestion trades off the size of the customer base and the speed of service. I show that profit-maximization leads to excessively slow service, providing an explanation for long lines in economic applications.

ABSTRACT. We consider repeated strategic interactions where individuals take two kinds of actions. In the moment, they repeatedly make competitive investments to appropriate recurring rivalrous resources. Over time, they invest into lobbying activities to change the competitiveness of the environment. Environments vary with respect to (i) the competitiveness of the environment (endogenously) and (ii) the degrees of foresight and asymmetry in contest efficacy amongst competitors (exogenously). The main contribution of our study is to show how the long-run stable levels of the former (i) dynamically depend on the latter (ii). Our model predicts correspondences between these factors, and quantifies the resulting social loss due to rent-seeking for each case.

ABSTRACT. This paper analyzes a contest in which rivals cannot observe each other's effort decisions.The designer maximizes discounted aggregate effort by choosing a starting time and a deadline of the contest. At the deadline, the contestant who exerted most effort wins a prize, which consists of the endowment of the designer plus collected interest.

I determine the Nash equilibria of the contest for all possible choices of starting time and deadline. The combination which maximizes discounted aggregate effort is characterized in closed form. I consider several extensions such as different types of asymmetries, a different contest success function and a different goal function of the designer.

ABSTRACT. In repeated contests with private information, weak contestants prefer to appear strong while strong contestants prefer to appear weak. In contrast to a single contest, this leads to an equilibrium where effort is not strictly monotonic in ability and allows for a less able contestant to win against a contestant of higher ability. While the aggregate payoffs of contestants are higher per contest than in the single contest benchmark, aggregate output per contest is lower. Depending on the economic setting, the presence of private information can lead to productive or allocational inefficiencies.

ABSTRACT. Standard results on and algorithms for repeated games assume that defections are instantly observable. In reality, it may take time for the knowledge that a defection has occurred to propagate through social networks. How does this affect the structure of equilibria and algorithms for computing them? In games with cooperation and defection, we prove that there exists a unique maximal set of forever-cooperating agents in equilibrium and give an efficient algorithm for computing it. Through simulations with random graphs, we observe a phase transition between cooperation everywhere and defection everywhere, based on the value of cooperation and the discount factor. We give an analytical expression for where the phase transition occurs and prove its accuracy (in the limit). Finally, we provide a condition for when the equilibrium found is credible, in that agents will in fact punish deviating agents. This condition always holds in our simulations, for sufficiently large graphs.

ABSTRACT. We analyze Social Storage systems based on strategic network formation games. Given the disk-failure-rate and the cost to add and maintain links, we define utilities of players in two frameworks, one where costs to add and maintain links are considered in the utility and another where budget constraints are considered. We, then, adapt the pairwise stability concept for Social Storage where both addition and deletion of links require mutual consent. We prove that, for symmetric storage networks with N players, there exists a unique stability point n. That is, all players try to achieve degree n. In particular, if N or n is/ are even, and if N > n, then n-regular networks on N vertices are the only stable Social Storage networks, unique up to isomorphism. We provide conditions for a Social Storage network to be stable, in general, and also discuss the number of non-isomorphic stable networks.

ABSTRACT. Paradox of choice occurs when permitting new strategies to some players yields lower payoffs for all players in the new equilibrium via a sequence of individually rational actions.

We consider social network games. In these games the payoff of each player increases when other players choose the same strategy.

The definition of games on social networks was introduced by K. Apt and S. Simon. In an article written jointly with E. Markakis, they considered four types of paradox of choice in such games and gave examples of three of them. The existence of paradoxical networks of the fourth type was proven only in a weakened form. The existence of so-called vulnerable networks in the strong sense remained an open question.

In the present paper we solve this open question by introducing a construction, called a cascade, and use it to provide uniform examples for all four definitions of paradoxical networks.

ABSTRACT. I analyze a model of fads. A fad is when a choice with no intrinsic value becomes popular, then unpopular. For example, in the 1960s, tailfins on cars were popular, in the 1970s, they were not. In the model, fads are driven through the channel of imperfect information. Some players have better information about the past actions of other players and are interested in communicating this through their own action choices. I show that in equilibrium, better informed players initially pool on a single action choice. Over time, the rest of the players learn which action the better-informed players are pooling on, and start to mimic them. Once a ‘tipping point’ is reached, the better-informed players switch to a different action, and the process repeats.

ABSTRACT. This paper proposes a model of rational attention allocation. An agent chooses between attention strategies to maximize her expected utility in a choice between two options. The optimal choice is given stochastically and the processing of information is costly. An attention strategy specifies which and in which order pieces of information are processed. Results demonstrate the superiority of three attention strategies: inattention, direct selection of decisive information, and a more complex conditional selection. This provides a rational foundation for bottom-up and top-down control of attention, reported in the psychological literature. Further, attention is context dependent and and low processing costs do not guarantee processing. Strategic considerations of the supply side reveal an incentive to produce the opposite quality of what agents expect and opportunities to exploit agents.

ABSTRACT. This article develops a general method to solve dynamic models of interactions between multiple strategic agents. It describes a general model of several interacting agents, their domination relations and a graph encoding their information pattern. It provides a general resolution algorithm and discusses the dynamics around the equilibrium. Our model explains apparent irrational or biased individual behaviors as the result of the actions of several goal-specific rational agents. In a three-agent model describing « the conscious », « the unconscious », and « the body », we show that, when the unconscious strategically dominates, the equilibrium is unconscious-optimal, but body and conscious-suboptimal. Our results allow for a precise account of agents’ time rate preference. Myopic behavior among agents leads to oscillatory dynamics. This describes cyclical and apparently inconsistent or irrational behaviors in the dual agent.

ABSTRACT. The present paper incorporates unawareness of decision criteria into multicriteria games. This is also an extension of single-criterion games with unawareness to the multicriteria case, though I focus only on unawareness of criteria. Generalized Pareto equilibria are defined as the equilibrium concept of the extended framework. The equilibria coincide with generalized Nash equilibria of weighted games with unawareness and their existence is proved. I also discuss how unawareness of criteria may change the set of equilibria with some illustrative examples.

ABSTRACT. This talk has been cancelled.

ABSTRACT. This paper extends the Harsanyi types model of beliefs to games in which there can be both negligble and nonneglible players. A universal type space exists in which every other type space can be uniquely embedded. The abstract types model is then used to explicitely characterize rationalizability, suitably formulated, as behavior compatible with common knowledge of rationality.

ABSTRACT. We provide a new modus operandi for the computation of the nucleolus in cooperative games with transferable utility. Using the concept of dual game we extend the theory of characterization sets. Dually essential and if the game is monotonic dually saturated coalitions determine both the core and the nucleolus whenever the core is non-empty. We show how these two sets are related to the existing characterization sets. In particular we prove that if the grand coalition is vital then the intersection of essential and dually essential coalitions forms a characterization set itself.

ABSTRACT. The assignment game (Shapley and Shubik, 1972) is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the good. The potential profit obtained by a buyer and a seller if they trade can be represented in a matrix, the assignment matrix. We show that the family of assignment matrices which give rise to the same nucleolus form a compact join-semilattice with one maximal element, which is always a valuation (see p.43, Topkis (1998) ). We give an explicit form of this valuation matrix. The above family is in general not a convex set, but path-connected, and we construct minimal elements of this family. We analyze the conditions to ensure that a given vector is the nucleolus of some assignment game. We study a specific rule to compute the nucleolus in some cases.

ABSTRACT. Least square prenucleolus is one of the important solutions of cooperative games. The main purpose of this paper is to extend it to interval cooperative games. In this method, through adding some weaker coalition monotonity-like conditions, it is proven that the least square prenucleolus of cooperative games is a monotonic and non-decreasing function of coalitions’ values. Hence, we can respectively obtain the lower and upper bounds of the interval least square prenucleolus, which form the interval least square prenucleolus of interval cooperative games. Hereby, we develop the concept of interval least square prenucleolus of interval cooperative games and its simplified method. The method proposed in this paper does not use the Moore’s interval subtraction and hereby can effectively overcome the issues resulted from the Moore’s interval subtraction. Moreover, real numerical examples are used to demonstrate the feasibility and applicability of the method proposed in this paper.

ABSTRACT. Two traditional paradigms describe the behavior of agents in multi-agent complex systems: full rationality (systems seen as multi-player games) and full stochasticity (systems seen as large stochastic processes). From the standpoint of a particular agent having to choose a strategy, the choice of the paradigm is crucial: the most adequate strategy depends on the assumptions made on the other agents.

In this paper, we focus on two-player games and their application to the automated synthesis of reliable controllers for reactive systems. In this setting, the system to control is a player, and its environment is its opponent, usually assumed to be fully antagonistic or fully stochastic. We illustrate several recent developments aiming to breach this narrow taxonomy by providing formal concepts and mathematical frameworks to reason about richer behavioral models. We illustrate those novel models on a classical challenge of the everyday life: planning a journey in an uncertain environment.

ABSTRACT. In this paper, we revisit a result by Jurg et al. (1990) where the necessary and sufficient condition for a bimatrix game to be weakly completely mixed is given. We present an alternate proof of this result using linear complemenatrity approach. We extend this result to a generalization of bimatrix game introduced by Gowda and Sznajder (1996) via a generalization of linear complementarity problem introduced by Cottle and Dantzig (1970). We further study completely mixed switching controller stochastic game (in which transition structure is a natural generalization of the single-controller games) and extend the results obtained by Filar (1985) for completely mixed single controller stochastic game to completely mixed switching controller stochastic game.

ABSTRACT. A major area of research in the field of stochastic games is to identify those classes of zero-sum stochastic games for which there is a possibility of obtaining a finite step algorithm to compute a solution. These classes are referred in the literature as structured stochastic games. For a class of structured stochastic games, it is known that optimal stationary strategies exist and that the value vector and optimal stationary strategies satisfy the ordered field property. In this paper, we discuss the problem of computing the value vector and stationary strategies for the class of stochastic game with special structure as a linear complementarity problem (vertical linear complementarity problem) and obtain sufficient conditions for solvability using Lemke's algorithm or Cottle-Dantzig's algorithm (a generalization of Lemke's algorithm). We also discuss some open problems that arises in complementarity formulation associated with structured stochastic game.

ABSTRACT. This paper considers the contracting issue of an innovation project between a principal and a team of agents where experimentation is required to explore the state of world. How many agents to hire is primary concern of the principal as the project is initiated. The decision could be made as if the principal takes entire expected payoff of the project into consideration. The model shows that the principal tends to hire less agents in correspondence to his downward-adjusted belief. And the principal's time preference alters his hiring choice. Patient principal would hiring less agents initially and experiments longer compared to impatient ones. To deal with the prevalent free-rider problem, the principal could charge each agent a certain price upfront given that a huge bonus would be provided as long as any one of them makes a success. Under this contract, the principal would benefit from extracting the entire surplus.

ABSTRACT. We study the role of information exchange, leadership, and coordination in team or partnership structures. For this purpose, we view individuals jointly engaging in productive processes---a 'team'---as endowed with individual and privately held information on the joint production process. Once each team member decided on whether or not to share their private information truthfully, they individually choose which effort to exert in the joint production process. This effort, however, is not contractible; only the realized output (or profit) of the team can be observed. Our central question is whether or not incentives can be provided to a team in this environment such that team members communicate their private information and exert efficient productive efforts on the basis of this communication. Our main result shows that there exists a simple ranking-based contract which implements both desiderata in a wide set of situations.

ABSTRACT. Collecting truthful subjective information from multiple individuals is an important problem in many social and online systems. While peer prediction mechanisms promise to elicit truthful information by rewarding participants with carefully constructed payments, they also admit uninformative equilibria where coordinating participants provide no useful information. To understand how participants behave towards such mechanisms in practice, we conduct the first controlled online experiment of a peer prediction mechanism, engaging the participants in a multiplayer, real-time and repeated game. Using a hidden Markov model to capture players’ strategies from their actions, our results show that participants successfully coordinate on uninformative equilibria and the truthful equilibrium is not focal, even when some uninformative equilibria do not exist or are undesirable. In contrast, most players are consistently truthful in the absence of peer prediction, suggesting that these mechanisms may be harmful when truthful reporting has similar cost to strategic behavior.

ABSTRACT. We propose definitions of substitutes and complements for pieces of information (“signals”) in the context of a decision problem. Informational substitutes capture diminishing marginal value of information, while complements capture increasing marginal value, with respect to a particular decision or prediction problem. The main application is to information aggregation in prediction markets, which are toy models for financial markets. We show a broad characterization: Substitutes characterize existence of “good” market equilibria where information is immediately aggregated, while complements capture existence of “bad” or trivial equilibria where the efficient market hypothesis fails. This broadly generalizes previous results.

We additionally examine the algorithmic problem of information acquisition under constraints, showing efficient algorithms when signals are substitutes, but computational hardness in general. The total set of results and characterizations give some evidence that, in parallel with substitutable goods, informational substitutes play a natural role in some fundamental contexts.

ABSTRACT. We study the economic rationale of the use of auctions and posted price selling mechanisms for the simultaneous allocation of on-line services having the infrastructure as a service public cloud computing market as a motivating example. By offering both selling mechanisms, the monopolist of a homogeneous good can discriminate among buyers of different private valuations. Auctioning the services can be designed so as to incorporate the risk for the winners of losing access to their service while it is still in operation. The posted price can by construction eliminate that risk. Buyers of high valuations prefer to pay a risk premium and get the service through the posted price mechanism while buyers of low valuations unable to meet the price level of the risk premium enter the auction. This is the optimal selling mechanism when the cost of interruption in the auction is high affects primarily the high valuation buyers.

ABSTRACT. We consider a multi-dimensional screening problem of selling a product with multiple quality levels. We show that only offering the highest quality is the revenue optimal mechanism if high valued customers are relatively less sensitive to quality. Our main methodological contribution is a framework to design multi-dimensional virtual values. A challenge of designing virtual values for multi-dimensional agents is that a mechanism that pointwise optimizes virtual values resulting from a general application of integration by parts on arbitrary paths is not incentive compatible. We resolve this issue by imposing additional restrictions on the problem so that the virtual value for the high quality product is uniquely defined, which pins down the paths and, consequently, the virtual values for other products. As a second application we use our method to derive conditions of optimality for selling only the grand bundle of items to an agent with additive preferences.

ABSTRACT. This study explores the effects of communication and its interaction with reputation information. Our focus is on buyer-determined procurement auctions with moral hazard in which buyers can select a bidder based on prices and all other information available. The results of our laboratory experiment demonstrate that – in contrast to reputation information – communication only slightly increases market efficiency. If reputation information is available, communication has no additional efficiency effect. Buyers' choice of a bidder is influenced by both, reputation information and the content of communication. Specifically, buyers prefer bidders with a good reputation and bidders who promise them a specific profit. If this kind of promise is infeasible – as it is often the case in real auctions, buyers prefer bidders whose arguments reduce social distance. Unspecific promises have no significant effect. In the field we find a choice pattern that is consistent with our lab data.

ABSTRACT. We study the effects of corruption on equilibrium competition and social welfare in a public procurement auction. A bureaucrat runs the auction on behalf of a government. He invites firms into the auction at positive costs, and may request a bribe from the winning firm afterward. We first show that, under standard assumptions, in the absence of corruption, the bureaucrat invites more firms than social optimum number that maximizes social welfare. Secondly, the effects of corruption on competition and social welfare vary across different forms of bribery. In the case of fixed bribe, corruption has no effect on equilibrium competition, yet does induce social welfare loss due to the distortion cost of increased public spending. In the case of proportional bribe, the corrupt bureaucrat will invite less firms into the auction, which may result in Pareto-improving allocation in equilibrium.

ABSTRACT. We consider stable licensing schemes that are combinations of lump-sum fee and per-unit royalty realized as bargaining outcomes in transferring a new technology of a technology holder to oligopolistic firms through licensing. Our solution concept is the rejection-proof core for each group of licensees, which is defined as a set of licensing schemes from which no coalition has an incentive to deviate credibly. We show that, for the group of licensees that maximizes the sum of the technology holder's profit and licensees' total surplus, the rejection-proof core is always non-empty. Further, the non-empty rejection-proof cores suggest that it should be optimal for the technology holder to license the new technology to such a group from the viewpoint of his profit maximization.

ABSTRACT. We study investments in R&D and the formation of R&D clusters of firms who are competitors in the market. In a three stage game, firms first decide on investments in R&D, then form research clusters and finally compete in quantities. We show that for any distribution of R&D investments, the second stage cluster formation modeled by the unanimity game (Bloch, 1996) has an equilibrium which is generically unique up to a permutation of firms who chose the same investment. Restricting to two investment strategies in the first stage, we provide a complete characterization of the equilibria of the three stage game. We show that for some range of investment costs equilibria with no-investment co-exist with equilibria where a large fraction or even all firms invest in R&D. Furthermore, in the high-investment equilibrium firms over-invest compared to a scenario with fixed clusters and to the welfare optimum.

ABSTRACT. We investigate the optimal job design in a repeated principal-agent relationship with multiple tasks where the performance measurement is distorted, aggregated, and nonverifiable. We compare task bundling where all the tasks are assigned to a single agent with task separation where the tasks are split and assigned to two agents. Compared to task bundling, task separation mitigates misallocation of efforts among the tasks but requires more commitment due to dispersion of informal bonuses to multiple agents. As a result, task separation is better than task bundling if and only if the discount factor of the parties is high. We also consider an extended model in which the principal combines explicit incentive pays based on a verifiable, distorted, and aggregated signal. In such cases, task separation is optimal if the discount factor is sufficiently high or sufficiently low.

ABSTRACT. In a principal-agent relationship in which the agent's type is correlated with an ex post signal, the principal may attain first best if she offers a lottery such that each type is rewarded for one signal realization and punished equally for all the others (Riordan and Sappington, 1988). When the agent is protected by limited liability, this kind of lottery is most likely to satisfy local incentive constraints (Gary-Bobo and Spiegel, 2006). We show that a different lottery, including three levels of profit (rather than two), is most likely to attain global incentive-compatibility if local incentive constraints are strictly satisfied. We identify conditions under which first best is implemented and pin down the optimal distortions when those conditions are violated. When the first-best allocation is locally but not globally incentive-compatible, output distortions are induced but no information rent is conceded.

ABSTRACT. We characterize optimal reward-based crowdfunding where production is contingent on an aggregate funding threshold. Crowdfunding adapts project implementation to demand (market-testing) and its multiple prices enhance rent-extraction via pivotality, even for large crowds, indeed arbitrarily large if tastes are correlated. Adaptation raises welfare. Rent-extraction can enhance adaptation, but sometimes distorts production and lowers welfare. Threshold commitment, central to All-Or-Nothing platforms, raises profits but can lower consumer welfare. When new buyers arrive ex-post, crowdfunding's market-test complements traditional finance and optimizes subsequent pricing. We prove that crowdfunding is a general optimal mechanism in our baseline.

ABSTRACT. We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions are necessary for SSPE but insufficient because these equations can be singular. Strategy profiles excluding perpetual disagreement guarantee non-singularity. The necessary and sufficient conditions for existence of stationary best responses additionally require either an equalizing condition or a minimality condition. Quasi SSPE only satisfy the recursive equations and optimality conditions. These always exist and are SSPE if either all equalizing conditions or all minimality conditions hold

ABSTRACT. This paper studies the Rubinstein bargaining game, in which both agents have reservation values. Agents are uncertain whether their opponents have high or low reservation values. Each agent tries to convince the other that he has a high reservation value, resulting in a unique war of attrition, as in the reputation literature. I analyze the information sensitivity of delay when agents publicly observe some noisy signal about their opponents’ reservation values. A bargaining environment is said to be more transparent if the available information is more precise. I show that information disclosure increases delay, in the sense of first-order stochastic dominance, if transparency is not sufficiently high. This paper also analyze the scope of intermediation in bargaining from an information designs perspective.

ABSTRACT. A seller negotiates price with a buyer who has an outside option that arrives at a random time during the negotiation. Both the buyer’s valuation of the good and the value of the outside option are unknown to the seller. We show that the interplay between information asymmetry and outside options is a source of delay in bargaining. In the seller-optimal bargaining mechanism, the seller and the buyer delay in reaching an agreement with positive probability; neither offers and counter-offers being exchanged nor the outside option being exercised while the parties wait. A delay occurs even in the limit as the arrival rate of the outside option grows to infinity. If the seller cannot commit to the seller-optimal bargaining mechanism, the same outcome is approximately achieved in a perfect Bayesian equilibrium of the bargaining game in which the seller makes all offers.

ABSTRACT. Voluntary contribution games are a classic social dilemma where the individually dominant strategies result in a poor performance of the population. The negative zero-contribution predictions from social dilemma situations give way to more positive (near-)efficient ones when assortativity, instead of random mixing, governs the matching process in the population. Under assortative matching, agents contribute more than what would otherwise be strategically rational in order to be matched with others doing likewise. An open question has been the robustness of such predictions in terms of provisioning of the public good when heterogeneity in budgets amongst individuals is allowed. Here, we show analytically that the consequences of permitting heterogeneity depend crucially on the exact nature of the underlying public-good provision efficacy, but generally are rather devastating. Using computational methods, we quantify the loss resulting from heterogeneity vis-a-vis the homogeneous case as a function of the public-good provision efficacy and the population inequality.

ABSTRACT. I propose the endogenous-priority student placement problem to study a centralized matching problem between students and schools, where the priorities of students are endogenous in terms of their efforts. With the motivation that in a desirable effort allocation students should allocate more efforts on the subjects that they are more talented at, I propose several notions of promoting diversity of talents including promoting versatility of talents, promoting unique talents, promoting n-selective talents and their variations. These notions differ in terms of degree of specialization. I also design matching systems that satisfy these notion. For the matching programs that I survey, most of them satisfy one of the notions that I propose. Finally, I study the matching programs in Taiwan in 2014 that match students to high schools and find that the features of the programs could encourage students to accumulate their human capital in a lexicographic manner.

ABSTRACT. The paper considers a one-to-one matching with contracts model in the presence of price controls. This set-up contains two important streams in the matching literature, those with and those without monetary transfers, as special cases and allows for intermediate cases with restrictions on the monetary transfers that are feasible. An adjustment process that ends with a stable outcome is presented, thereby proving the existence of stable outcomes. The process contains the deferred acceptance algorithm of Gale and Shapley (1962) and the approximate auction mechanism of Demange, Gale, and Sotomayor (1986) as special cases. The paper presents a notion of competitive equilibrium for this class of models, called Drèze equilibrium, thereby extending the concept as developed by Drèze (1975) for economies with divisible commodities subject to price controls. It is shown that Drèze equilibrium allocations are equivalent to allocations induced by stable outcomes.

ABSTRACT. We study rules for allocating objects. Departing from standard analysis, we evaluate rules according to their performance at an ex-ante stage, before individuals learn their preferences. Introducing an appropriate notion of ex-ante efficiency, we search for rules that are both efficient and provide incentive for individuals to truthfully report their eventual preferences. Our main results characterize the priority (``serial dictatorship'') rules by ex-ante efficiency and either strategy-proofness or Bayesian incentive compatibility on natural preference domains. When behind the veil, agents and objects are indistinguishable. In this setting, all rules in a large family achieve the same utilitarian welfare, and the family admits Lorenz maximal and minimal elements. Allowing the size of the economy to grow, we find that average welfare under each rule approaches that of a utilitarian rule. Comparing further, we introduce solidarity properties and consider an interim participation constraint. These considerations distinguish methods of randomizing over families.

ABSTRACT. We study social decision schemes (SDSs), i.e., functions that map individual preferences over alternatives to a lottery over the alternatives. Depending on how preferences over alternatives are extended to preferences over lotteries, there are varying degrees of efficiency and strategyproofness. In this paper, we consider four such preference extensions: stochastic dominance (SD), a strengthening of SD based on pairwise comparisons (PC), a weakening of SD called bilinear dominance (BD), and and even weaker extension based on Savage's sure-thing principle (ST). While random serial dictatorships are PC-strategyproof, they only satisfy ex-post efficiency. On the other hand, we show that strict maximal lotteries--a little known class of SDSs due to Fishburn--satisfy PC-efficiency and ST-strategyproofness. The incompatibility of SD-efficiency and SD-strategyproofness was recently shown using computer-aided solving techniques. We provide a manual proof of the the same statement using the PC extension. Finally, we show that no SDS satisfies ex-post efficiency and SD-group-strategyproofness.

ABSTRACT. This talk has been cancelled.

ABSTRACT. Cooperative differential and dynamic TU games with prescribed duration are considered. Different approaches to the definition of characteristic function are proposed. One of basic problems in considered class of games is time-inconsistency of solution concepts taken from classical cooperative game theory. This problem is partly solved by introduction of IDP (imputation distribution procedure) but in the case when solution does not consist of unique imputation a more stringent condition of strongly time-consistency (STC) for sustainable cooperation is necessary. Unfortunately the class of games in which this stringent condition holds is very limited. To overcome this difficulty different approaches are proposed. Among them integral transformation of characteristic function and two refinements of STC (with weaker conditions). The sufficient conditions for the existence of strongly time-consistent (in weak sense) core and other solutions are derived. The proposed approach can be easily extended to discrete-time cooperative dynamic games.

ABSTRACT. The report is concerned with two-person dynamic zero-sum games in continuous setting. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value functions of λ-discounted games as the discount tends to zero. Under quite weak assumptions on the game, we prove the Uniform Tauberian Theorem: existence of a uniform limit for one of the value functions implies the uniform convergence of the other one to the same limit. We also prove the analogs of the One-sided Tauberian Theorem, i.e., the inequalities on asymptotics for the lower and upper games. Also, a variant of the theorem for discrete-time games is treated separately. Special attention is devoted to the case of differential games.

ABSTRACT. We obtain a characterization of subgame–perfect equilibrium plays in a class of perfect information games under the assumption that each player’s payoff function is Borel measurable and has a finite range. The set of subgame–perfect equilibrium plays is obtained through a process of iterative elimination of plays. Extensions to games with bounded Borel measurable payoff functions are discussed. As an application of our results, we show that if every player’s payoff function is bounded and upper semicontinuous, then, for every positive epsilon, the game admits a subgame–perfect epsilon–equilibrium. As we do not assume that the number of players is finite, this result generalizes the corresponding result of Purves and Sudderth [2011].

ABSTRACT. We show generically that the Purification Theorem of Harsanyi (1973) does not hold for 2 x 2 games without the assumption of common knowledge of priors. We obtain that the limit of the Mirage Equilibrium - the corresponding generalization of Bayesian Equilibrium - of the perturbed game does not coincide with the mixed strategy equilibrium of the unperturbed game, rather it yields a pure strategy.

ABSTRACT. In this paper, we study a 2 by 2 strategic-complements Bayesian entry game with correlated private information. The distribution of private information is modelled by a bivariate normal distribution. We examine the comparative statics of the model, indicating how the number of equilibrium varies with the correlation coefficient and variances of the prior distribution. We show that Harsanyi's (1973) purification theorem can be extended to games with dependent perturbation errors that follow a normal distribution if the correlation coefficient is positive for the strategic complements games or negative for the strategic substitutes games.

ABSTRACT. We study collusion within groups in non-cooperative games. The primitives are the preferences of the players, their assignment to non-overlapping groups and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Such equilibria need not exist. We introduce the notion of collusion constrained equilibrium, which allows randomizations by groups between alternatives to which they are not indifferent. Collusion constrained equilibria always exist and are a subset of the correlated equilibria of the underlying game. We examine three perturbations of the underlying game. In each case we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria. Finally we show that for a broader class of perturbations every collusion constrained equilibrium arises as such a limit.

ABSTRACT. In this paper, we investigate the dynamic decision making problem when there are a set of linear constraints on the empirical frequency of actions actually played. To cope with this, we introduce the constrained no-regret learning model. In this model, the set of alternative strategies, with which a dynamic decision mechanism is compared, is the set of stationary mixed actions that satisfy the set of linear constraints. We show that there is indeed a constrained no-regret dynamics.

ABSTRACT. The first ever human vs. computer no-limit Texas hold 'em competition took place from April 24 to May 8, 2015 at River's Casino in Pittsburgh, PA. In this article I present my thoughts on the competition design, agent architecture, and lessons learned.

ABSTRACT. In a search for a positive model of decision-making with observable primitives, we rely on the burgeoning literature in cognitive neuroscience to construct a three-element machine (agent). Its control unit initiates either impulsive or cognitive element to solve a problem in a stationary Markov environment, the chosen element depends on the nature of the problem, memory of past successes and inhibition.

Our predictions are based on a stationary asymptotic distribution of the memory, which can generate different ``characters'', e.g., an uptight dimwit, who could succeed more often with less inhibition, as well as a relaxed wise-guy, who could gain more with a stronger inhibition of impulsive (intuitive) responses.

As one would expect, stronger inhibition and lower cognitive costs increase the frequency of decisions made by the cognitive element. More surprisingly, increasing the ``carrot'' and reducing the ``stick'' enhances contemplative decisions for an alert agent, who identifies novel problems frequently enough.

ABSTRACT. This paper studies beauty-contests with rationally inattentive players. Players are driven by a coordination motive and a fundamental motive. Each player can flexibly acquire information on the fundamental by choosing the probability distribution of her signal while paying a cost linear in the reduction of entropy. A necessary condition is derived for well-behaved equilibria without requiring the fundamental to be normally distributed. Aggregately affine equilibria (AAE) where the average action is an affine function of the fundamental are found to exist only if the fundamental is normally distributed. For a large region of the parameter space, there exists a unique equilibrium within the classes of AAE and equilibria without information acquisition. Interestingly, when the coordination motive is high and for relatively low information costs, there is a multiplicity of equilibria within the classes considered, suggesting that flexible information acquisition technology can be a source of multiple equilibria.

ABSTRACT. We conduct an experiment to uncover the reasons behind the typically large behavioural variation and low explanatory power of Nash equilibrium observed in Tullock contests. In our standard contest treatment, only 7% of choices are consistent with Nash equilibrium which is in line with the literature and roughly what random (uniform) choice would predict (6.25%). We consider a large class of social, risk and some other 'non-standard' preferences and show that heterogeneity in preferences cannot explain these results. We then systematically vary the complexity of both components of Nash behaviour: (i) the difficulty to form correct beliefs and (ii) the difficulty to formulate best responses. Our results show that bounded rationality rather than heterogeneity in preferences is the reason behind the huge behavioural variation typically observed in Tullock contests.

ABSTRACT. We consider contests in which two opponents with different initial strengths have the option to make spot allocations to enhance their performance. We allow the prize to depend on total performance in the contest and consider the respective cases in which efforts are productive and destructive of prize value. When the contest success function takes a logit form, and marginal cost is increasing in effort, we show that a Nash equilibrium exists and is unique both in productive and destructive endogenous prize contests. In a productive contest, the underdog behaves more aggressively and wins the prize more often in comparison to a fixed value contest. These results have implications for the understanding of a variety of phenomena in which the value of the prize is endogenous, including (asymmetric) armed conflict, litigation, sports contests, R&D races, and labor tournaments.

ABSTRACT. This paper analyzes the incentives that arise within an organization when communication is restricted to a particular network structure (e.g., a hierarchy). We show that restricting communication between the principal and agents may create incentives for the agents to misbehave when transmitting information and tasks throughout the organization. To remedy this issue, we provide necessary and sufficient conditions on the topology of the network of communication such that restricting communication to a particular network does not restrict the set of outcomes that the principal could otherwise achieve. We show that for any underlying incentives and any outcome available when communication is unrestricted, there exists a communication scheme restricted to a particular network that implements this outcome (i.e., does not induce agents to misbehave in the communication phase) if and only if that network satisfies our conditions.

ABSTRACT. This paper considers individuals who make predictions in new situations using categories. We present a framework to examine when decision makers may be better off using fewer rather than more categories even without exogenous costs or restrictions concerning the number of categories available. We study three aspects of this problem: An individual whose goal is to predict the unobserved value of a new object correctly, individuals who want to coordinate their predictions with each other, and individuals who are interested in both. We analyze the effect of the coordination motive on individual categorization and we show that the attempt to coordinate with others can be a rationale to categorize coarsely.

ABSTRACT. We present a flexible model of wage dynamics where information about job openings is transmitted through social networks. The model is based on Calvo-Armengol & Jackson (2004, 2007) and extends their results outside the stationary distribution, and under observed and unobserved heterogeneity. We present an empirical application using the British Household Panel Survey by exploiting direct information about individual’s social networks. We find that the distribution of job offers is positively affected by the employment status of an individual’s friends, and that this relationship is stronger for women.

ABSTRACT. Rational secret sharing was proposed in STOC'04. The authors show that, in a setting with rational parties, secret sharing is only possible if the actual secret recovery round remains unknown to the players. We change the direction by bridging cryptography, game theory, and reputation systems, and propose a social model for repeated rational secret sharing. We provide a new scheme, named socio-rational secret sharing, in which players are invited to each game based on their reputations, i.e., they run secret sharing protocols while sustaining a public trust network. As a result, new notions such as a rational foresighted player, social game, and social Nash equilibrium are introduced. To motivate our approach, consider a repeated game such as sealed-bid auctions. If we assume each party has a reputation value, we can penalize (reward) the players who are selfish (unselfish) from game to game. This social reinforcement stimulates players to be cooperative.

ABSTRACT. We study perception biases arising under second-best perception strategies. An agent's type is either high or low, and accurate perception of one's type is costly. A perception strategy specifies the probabilities of the two types of perception errors. After the true and perceived types are realized, the agent faces a random decision problem. Payoffs depends on types as well as choices and thus misperceptions distort choice. We say that the high type has more control over her payoffs than the low type if the payoff difference across actions is likely to be large for the high type and small for the low type. As elimination of perception errors is costly, the optimal strategy exhibits an illusion of control---the probability that the agent perceives her type as high exceeds the true probability of the high type. We show in examples that the effect generates overconfidence about talent or knowledge, and optimism.

ABSTRACT. This talk has been cancelled.

ABSTRACT. We consider two-player zero-sum games with infinite action spaces and bounded payoff functions. The players' strategies are finitely additive probability measures, called charges. Since a strategy profile does not always induce a unique expected payoff, we distinguish two extreme attitudes of players. A player is viewed as pessimistic if he always evaluates the range of possible expected payoffs by the worst one, and a player is viewed as optimistic if he always evaluates it by the best one. This approach results in a definition of a pessimistic and an optimistic value for each player. We provide an extensive analysis of the relation between these values, and connect them to the classical values, and to other known techniques to define expected payoffs, based on computation of double integrals. In addition, we also examine existence of optimal strategies with respect to these values.

ABSTRACT. The construction of the universal type space for conditional probability systems of Battigalli and Siniscalchi [Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games, J. Econ. Theory, 88 (1999) 188–230] is a fundamental ingredient for the epistemic analysis of dynamic games. In this paper we extend the construction to address simple unawareness, showing that the universal type space for the standard case is a special instance of the universal type space constructed here, where the perception of the domain of uncertainty that players have does not change.

ABSTRACT. We prove that a universal preference type space exists under more general conditions than those postulated by Epstein and Wang (1996). To wit, it suffices that preferences can be encoded monotonically in rich enough ways by collections of continuous, monotone real-valued functionals over acts, which determine—even in discontinuous fashion—the preferences over limit acts. The proof relies on a generalization of the method developed by Heifetz and Samet (1998a).

ABSTRACT. We revisit the solution of generalized stable sets for abstract decision problems. This solution was introduced by van Deemen (1991) as a variant of stable sets formulated in Von Neumann and Morgenstern (1944). Here, we propose an alternative characterization for generalized stable sets which may reveal the stability of generalized stable sets from a new perspective. Moreover, we compare the sensitivities of generalized stable sets and of stable sets to changes in the dominance relation. Finally, the collection of generalized stable sets may be very large in cyclic domains so that this solution may lose its power to discriminate among alternatives. As such, we refine this solution to select more discriminatory generalized stable sets.

ABSTRACT. We show that Harsanyi’s critique of vNM stable sets is not really valid and a subset of vNM stable sets are actually farsighted.To show this, we motivate and introduce an alternative concept of a stable set, to be called an infinitely farsighted stable set. The concept of an infinitely farsighted stable set is based on a new and more general notion of a credible deviation. According to this notion, a coalition may not only deviate from a deviant coalition, but may also merge with some residual players. Thus, “objections” are not necessarily nested in the sense of coming from subsets of progressively smaller coalitions. After establishing the general properties of infinitely farsighted stable sets, we prove their existence and comprehensively characterize them for general three-player superadditive characteristic function games and also prove their existence for simple majority rule and convex games with any number of players.

ABSTRACT. We investigate the farsighted stable set in a class of strategic games with dominant punishment strategies. In this class of games, each player has a strategy that uniformly minimizes the other players' payoffs for any given strategies of other players. We particularly investigate a special class of the farsighted stable sets each of which consists of strategy profiles yielding an identical payoff vector. We call such farsighted stable sets as the single-payoff farsighted stable sets. We completely characterize the single-payoff farsighted stable sets in the strategic games with dominant punishment strategies by the notion of the inclusive set. We also show that the set of payoff vectors yielded by the single-payoff farsighted stable sets is closely related to the strict alpha-core in strategic games. Further, we apply the results to the binary choice strategic game and strategic games for many-to-many matching markets with substitutability.

ABSTRACT. How does freedom of information about an institution’s resilience affect its stability? We study the ex ante impact of an informative public signal on regime change in a global game, accounting for uncertainty over what will be communicated. We show that a fundamental tension exists in the way public information impacts coordination. When the probability of regime change is already high, public information systematically incentivizes larger attacks. But under these conditions public information targets attacks wastefully, causing agents to strike when the regime is so weak it would have fallen anyway and retreat when the regime is vulnerable to a larger attack. By way of a general decomposition, we sign the marginal impact of transparency on regime change in several applications.

ABSTRACT. An influential thesis often associated with De Tocqueville views social mobility as a bulwark of democracy: when members of a social group expect to join the ranks of other social groups in the near future, they should have less reason to exclude these other groups from the political process. In this paper, we investigate this hypothesis using a dynamic model of political economy. As well as formalizing this argument, our model demonstrates its limits, elucidating a robust theoretical force making democracy less stable in societies with high social mobility: when the median voter expects to move up (respectively down), she would prefer to give less voice to poorer (respectively richer) social groups. Our theoretical analysis shows that in the presence of social mobility, the political preferences of an individual depend on the potentially conflicting preferences of her future selves, and that the evolution of institutions is determined through the implicit interaction between occupants of the same social niche at different points in time. When social mobility is endogenized, our model identifies new political economic forces limiting the amount of mobility in society because the middle class will lose out from mobility at the bottom and because a peripheral coalition between the rich and the poor may oppose mobility at the top.

ABSTRACT. This paper seeks to understand the role of political institutions in influencing the evolution of human behavior. In the model, a political institution provides the platform and a set of rules for the agents to battle over the relative representativeness of their strategies for the high positions in the social hierarchy. Such a political process affects the agents' payoffs, subsequently the evolution of their strategies. We investigate evolutionarily stable strategies under an exclusive and an inclusive political institution. We find that an exclusive political institution induces self-interest behavior for the low positions agents. On the other hand, an inclusive political institution induces altruistic behavior for the high position agents while it induces spiteful behavior for the low position agents. We further show that the results are robust when evolution operates on the preference level with incomplete information.

ABSTRACT. Consider a social planner redistributes the net-benefits of connected public facilities (such as highways, rail-roads or irrigation canals) that can be built in different network configurations. Consider the planner has all information in the network and is interested in systematically selecting a path and share the surplus. We purpose four natural axioms and we show that they characterize a family of path selection rules that selects efficient path(s), and the surplus is distributed in fix proportions independent of the network. Alternatively, suppose the planner know the structure of the network but not the marginal benefits of paths. The planner wants to find a sharing rule that incentivizes the agents to select an efficient path as a subgame perfect equilibrium in some games. We show that for a large class of games, most of the rules obtained under incomplete information coincide with the rules found in the case of complete information.

ABSTRACT. The paper examines minimum cost arborescence problems, which generalize the well-known minimum cost spanning tree (mcst) problems. We propose a new family of cost sharing methods that are easy to compute, as they closely relate to the network-building algorithm. These methods, called minimum incoming cost rules for arborescences (MICRAs), include as a particular case the extension of the folk solution introduced by Dutta and Mishra (2012). A simpler computational procedure thus obtains for this method. We also provide new axiomatizations of (a) the set of stable and symmetric MICRAs and (b) the folk solution. Finally, we closely examine two remarkable MICRAs. The first one relates to the cycle-complete rule for mcst problems introduced in Trudeau (2012). The second one contrasts with the folk rule by fully rewarding agents who help others connect to the source.

ABSTRACT. We study the problem of transmission of a divisible resource to agents via a network of intermediaries. The planner has preferences over allocations of the resource to the agents. The planner is not directly linked to the agents but it can connect via intermediaries. Intermediaries differ in the types of agents they reach and the quality in which they reach agents.

The planner solicits bids from intermediaries to use their links and selects which intermediaries to contract for the transmission of the resource. The intermediaries choose the fees in order to maximize the amount paid by the planner. We analyse the strategic behavior of the planner and the intermediaries. Necessary and sufficient conditions for the existence of a Subgame Perfect Nash Equilibrium (SPNE) and Efficient SPNE are presented. This equilibrium depends on the network configuration, the quality of the intermediaries, and the planner's preferences.

ABSTRACT. The paper introduces activity systems as a general framework for modeling interaction and cooperation among agents, and analyses them through the tools of quantum theory. Remarkable examples of activity systems include classical coalitional games and networks of agents. In the former example, coalition formation and its evolution are the main problems we consider, while in networks activity systems are adequate to model influence among the agents. We introduce spectral decomposition of activity matrices, linear operators as well as waves and evolution of systems.

ABSTRACT. The aim of this paper is to develop a tau-value method for solving cooperative games with fuzzy coaltions, which is also referred as fuzzy cooperative games. In this method, using the multilinear extensive method, we define the tau-value for fuzzy cooperative games and prove its existence, uniqueness and other properties. Simple computational formulae of the tau-values for convex fuzzy cooperative games is deduced. Moreover, the relation between the tau-value and the fuzzy core is discussed. The research results show that the tau-value for the fuzzy cooperative game with multilinear extension form is an extension of the tau-value for crisp cooperative games. Especially, for the convex fuzzy cooperative games, the computational process of the tau-value can be further simplified.

ABSTRACT. This talk has been cancelled.

ABSTRACT. Matching problems are of central importance in many areas, including matching students to schools, interns to jobs in fields like law and medicine, and donors to patients in need of transplants. Many of these processes are centralized, or can be effectively centralized. Much of the work on such problems has focused on the design of such centralized exchanges and of algorithms for the implementation of matches with desirable properties. An important message in this work is that centralizing such exchanges with judicious market design can create large welfare gains. Other important matching problems instead take place in decentralized markets, including many labor markets and buyer-supplier markets. I will talk about a model that nests many common matching models within a general market framework, including one-to-one, many-to-one, and many-to-many matching, matching with contracts, and matching with incomplete information. I will talk about various decentralized equilibrium concepts for such markets and how these can shed light on properties of centralized exchanges as well.

ABSTRACT. We study a political contest between two groups. Two lobbying groups or political parties compete for a prize by providing or promising effort. We consider a number of different mechanisms for resolving the contest. Our focus is on groups of different sizes and when the larger or smaller group is more likely to be successful. Key to our results is the notion that effort provision might a duty or a chore. For example, if there is a ballot referendum against farm subsidies, while it is costly to go to the polling place and take time to vote I view it as my civic duty, so I vote and the satisfaction of having discharged my duty more than offsets the direct cost of participating. By contrast, to engage in an anti-farm lobby I would need to find the appropriate organization, learn about them, join up - and they would have to vet me, process my application and so forth. Considerable cost would be incurred even as I contributed nothing to the lobbying effort. This kind of fixed cost we refer to as a chore. Our main finding is that the mechanism makes little difference but that the structure of cost does: duty favors larger groups and a chore favors smaller groups.

Joint work with Andrea Mattozzi and Salvatore Modica.

ABSTRACT. Mean Field Games describe nonatomic games in continuous time. We describe a learning procedure for these games and show the existence of "stable equilibria" towards which the learning procedure converges.

Based on papers with Saeed Hadikhanloo and with Ariela Briani.

ABSTRACT. I will review some techniques that are used in the study of multiplayer stochastic games, present results that they prove and open problems that are waiting for solution. The techniques include the dynamic use of discounted equilibria, the dynamics of the Nash correspondence, and the stochastic Ramsey theorem.

ABSTRACT. Evolutionary dynamics model how a population of agents revise their strategies in reaction to shifting fitness levels. Depending on both the specific dynamics and underlying population game, long term behaviors can range from cycling to chaos to convergence, with convergence to Nash equilibrium of particular interest. One restriction of almost all evolutionary dynamics, (e.g., replicator dynamics, fictitious play, imitation dynamics, etc.) is that the number of state variables is equal to the number of population strategies. The introduction of auxiliary states, which results in higher order dynamics, can model effects such as latency, recency, or anticipation. Furthermore, prior work has shown that higher order dynamics can circumvent structural limitations of first order dynamics (e.g., uncoupled convergence to Nash equilibrium or dominated strategy elimination). This talk explores higher order dynamics from the perspective of so-called passive game dynamics. Passive dynamics are a class of evolutionary dynamics that complement the class of stable games (introduced by Hofbauer and Sandholm) in the sense that any passive game dynamic coupled with any stable game results in stable behavior. This perspective allows one to analyze both first order and higher order evolutionary dynamics in the same framework. Furthermore, it accommodates the analysis of higher order population games, where fitness levels exhibit path dependencies. We also show a sort of converse stability result: namely any evolutionary dynamic that stabilizes all (higher order) stable games must be passive.

ABSTRACT. We consider a simple model of neural decision making in which there is a limited capacity to make fine distinctions. This implies that the evolutionarily optimal hedonic utility function must adapt to the circumstances. The new result here is that there are readily implementable mechanisms by which utility functions adapt rapidly, in real time. That is, if the distribution of rewards shifts, the utility function reacts, to maintain optimal use of the limited capacity to discriminate. Such rapid adaptation of utility is analogous to well-known properties of the visual system, and might well be implemented by similar neural circuitry. In the case that all that matters is the probability of error, the mechanism is particularly simple. If the criterion is instead to maximize expected fitness, we find a mechanism that is approximately optimal.

Although such adaptive utility functions take an hedonic interpretation of preference seriously, and incorporate large swings in levels, they are at once approximately consistent with conventional economics. That is, the possibility of suboptimal choice stems only from the limited capacity to make fine distinctions. As this capacity improves, utility remains adaptive, but choice becomes fully optimal.

ABSTRACT. For selling a single item to agents with independent but non-identically distributed values, the revenue optimal auction is complex. With respect to it, Hartline and Roughgarden (2009) showed that the approximation factor of the second-price auction with an anonymous reserve is between two and four. We consider the more demanding problem of approximating the revenue of the ex ante relaxation of the auction problem by posting an anonymous price (while supplies last) and prove that their worst-case ratio is e. As a corollary, the upper-bound of anonymous pricing or anonymous reserves versus the optimal auction improves from four to $e$. We conclude that, up to an $e$ factor, discrimination and simultaneity are unimportant for driving revenue in single-item auctions.

ABSTRACT. Myerson derived a simple and elegant solution to the single-parameter revenue-maximization problem in his seminal work on optimal auction design, assuming the usual model of quasi-linear utilities. In this paper, we consider a slight generalization of this usual model---from linear to convex ``perceived'' payments. We study the optimal auction design problem using this form of utility function in two settings: the robust setting, where conditions must always hold, and the Bayesian setting, where conditions need only hold in expectation. We show that total expected revenue need not coincide in these two problems. In the Bayesian setting, we show that only polynomially-many, and not exponentially-many, payment variables are required. We derive bounds, based on which we develop easily computable heuristics that approximate optimal auction designs. Our experiments demonstrate that our heuristics find near-optimal solutions more quickly than standard mathematical programming solvers.

ABSTRACT. We study revenue maximization in settings where agents' values are interdependent: each agent receives a signal drawn from a correlated distribution and agents' values are functions of all of the signals. Previous work on characterizing optimal mechanisms in these settings requires many strong assumptions on the agents' value functions and value distributions. We introduce a variant of the generalized VCG auction with reserve prices and random admission, and show that this auction obtains strong revenue guarantees in ex-post equilibrium for any matroid environment. For value functions that are additively separable, our results require only a standard single-crossing property, but do not require any distributional assumptions. The results also hold in more general settings when the value functions satisfy a concavity-type condition.

ABSTRACT. Social psychologists have argued that the tendency to compare ourselves to others may generate competitive behavior. In economics, the experimental literature has demonstrated that bidding behavior in first-price and second-price auctions is more competitive than predicted by standard auction theory. We show that this behavior can be explained by assuming that bidders are concerned with social comparisons. We adopt a model of interdependent preferences, where bidders derive utility (pride) from being better off than others and derive disutility (envy) from being worse off than others. We find that anticipating envy is necessary to generate overbidding. Furthermore, the more envious a bidder is, the more she will overbid. Surprisingly, anticipating pride does not generate overbidding, but rather decreases bids to the levels predicted by standard auction theory. Our model further predicts that the second-price auction generates higher expected revenues than the first-price auction.

ABSTRACT. We performed controlled experiments of human participants in a continuous sequence of ad auctions, similar to those used by Internet companies. The goal of the research was to understand users' strategies in making bids. We studied the behavior under two auction types: (1) the GSP auction and (2) the VCG payment rule, and manipulated also the participants' knowledge conditions: (1) explicitly given valuations and (2) payoff information from which valuations could be deduced. We found several interesting behaviors: (1) No convergence to equilibrium was detected; (2) Explicit ``better-response'' behavior; (3) GSP bidders do strategically shade their bids, but they tend to bid higher than the standard VCG-like equilibrium of GSP. (4) Bidders who are not explicitly given their valuations behave a little less ``precisely'', but mostly during an initial learning phase. (5) VCG and GSP yield approximately the same (high) social welfare, but GSP tends to give higher revenue.

ABSTRACT. A major complaint of sellers in online auctions is that winning bidders often fail to pay and claim their item. Bids constitute a legally binding contract. Yet sellers can do little to enforce a bid. Instead, auction rules often allow sellers to approach the second-highest bidder with a `second-chance offer' -- a take-it-or-leave-it offer, to buy at this bidder's highest bid price. Furthermore, auction platforms also often let sellers leave negative feedback on a buyer. Both features however alter bidders' behavior in a way that imposes costs on sellers, as we show theoretically and by examining bidding in experimental auctions. All else equal, the availability of second-chance offers reduces bids. This lowers sellers' revenue also in auctions where no default occurs. In addition, buyer reputation systems create a strategic effect that rewards bidders who have a reputation for defaulting, counter to the idea of creating a deterrent against such behavior.

ABSTRACT. We study a horizontal differentiation model in which one of the two attributes of a product, product fit and price, is more salient for the consumer than the other. Which attribute is more salient depends on relative differences between the available products, and is determined endogenously as a result of firm strategies. We find that high (respectively, low) marginal costs soften (respectively, harden) price competition of firms. We also find cost over-shifting for some parameter values. Both industry- and firm-level cost increases may be beneficial for firms.

ABSTRACT. We study the market outcome that evolves in the long-run when price-setting firms, that compete in a differentiated market, are driven by an imitation dynamic. The prices that evolve in the long-run depend on market differentiation and on the degree of oversight firms have on market decisions and outcomes. The unique symmetric pure Nash equilibrium price is always supported in the long-run, and it is the unique long-run market outcome for high and low levels of differentiation, when there is no oversight or even with limited oversight on market decisions and outcomes. For intermediate levels of differentiation, in addition to the Nash equilibrium price, there is a set of prices that may emerge in the long-run: while these other prices are below Nash equilibrium price when there is (almost) no oversight on market performances, they are above Nash equilibrium price when the oversight on market performances is more acute.

ABSTRACT. In sequential screening problems local incentive compatibility constraints are sufficient for implementability under some regularity conditions and the assumption of first-order stochastic dominance or mean-preserving spread (Courty and Li, 2000). In a setting with four possible cost distributions, two with equal expected values and different spreads and two with different expected values and equal spreads, we show that local incentive constraints are sufficient only when the marginal surplus is sufficiently convex. We further suggest that, in the same vein as in Consumption theory, the contractual choice can be regarded as mirroring the preference of the decision-maker for a lottery that occasions a higher (certain) cost but grants the possibility of facing more efficient (random) outcomes. Resting on this interpretation, we assess that the benefit of screening the agent in two stages, rather than in the contracting stage only, is higher when the marginal surplus is less concave / more convex.

ABSTRACT. We study an optimal contract problem under moral hazard in a principal-agent framework where contracts are implemented through random auditing. This is a monitoring instrument which reveals the precise action taken by the agent with some nondegenerate probability r, and otherwise reveals no information. The agent's cost of performing the action depends on a random state of nature. This state is private information to the agent, but he can non-verifiably communicate it, allowing the contract to specify wages as a function of the agent's message. The optimal contract partitions the set of types in three regions. The most efficient types exert effort and receive a reward when audited. Moderately efficient types exert effort but are paid the same wage with an audit as without. The least efficient types do not exert effort. More intense monitoring increases the value of a contract when the agent is risk averse.

ABSTRACT. We study the competitive equilibria in a market with adverse selection and search frictions. Uninformed buyers post general direct mechanisms and informed sellers choose where to direct their search. We demonstrate that there exists a unique equilibrium allocation and characterize its properties: all buyers post the same mechanism and a low quality object is traded whenever such object is present in a meeting. Sellers are thus pooled at the search stage and screened at the mechanism stage. If adverse selection is sufficiently severe, this equilibrium is constrained inefficient. Furthermore, the properties of the equilibrium differ starkly from the case where meetings are restricted to be bilateral, in which case in equilibrium sellers sort across different mechanisms at the search stage. Compared to such sorting equilibria, our equilibrium yields a higher surplus for most, but not all, parameter specifications.

ABSTRACT. In a multilateral enforcement regime, a player who cheats on one partner is punished by many partners. But if partners can renegotiate in private, they can subvert the power of the multilateral punishment. We introduce a new notion of “bilateral renegotiation proofness” that applies to multilateral games with private monitoring. We characterize optimal bilateral renegotiation proof equilibria for a community engaged in bilateral joint production relation- ships. While players’ ability to renegotiate bilaterally is indeed socially costly, it is perhaps not as costly as one might expect. We show that the proportional cost imposed by bil

ABSTRACT. We analyze the problem of coalition formation and surplus division. We propose a new non-cooperative game in which at every period there is a coalition formation stage followed by a negotiation stage. In contrast with the canonical Baron and Ferejohn (1989) model, we show that our equilibrium has several desirable properties, such as, dummy players have zero value and are never included in coalitions that form, and the model does not rely on an exogenously given proposer probability. We characterize the Markov perfect equilibrium of the game and show that the limit equilibrium is one where the coalitions that form in equilibrium maximize the average gain of each coalition member. We also discuss several applications to weighted majority games, providing a complete characterization of the equilibrium for all weighted majority games with less than eight players, and solve for the equilibrium of the European Union Council.

ABSTRACT. Orthodox game theory is sometimes criticised for its failure to single out intuitively compelling solutions in certain types of interpersonal interactions. The theory of virtual bargaining provides a resolution in some such cases by suggesting a shift in decision-makers’ mode of reasoning from best-response reasoning to reasoning as hypothetical bargainers: hypothetical bargainers identify the strategy profiles that they would agree to realise via joint actions if they were engaged in open bargaining. I propose a general epistemic model of hypothetical bargaining, which suggests, how hypothetical bargainers may use the information about each other’s preferences over the strategy profiles of the game in identifying solutions of one-shot n-player non-cooperative games. I present an algorithm for identifying the hypothetical bargaining solutions of non-cooperative games, and show that suggested solution concept shares conceptual similarities with envy-free bargaining solution. I discuss the theoretical predictions of the model using a number of experimentally relevant examples.

ABSTRACT. We consider revenue maximization for a monopolistic matching platform. Specifically we consider markets where the platform controls the agents' ability to form pairs that yield nontransferable value. A platform posts prices and commits to a matching procedure---a function of the agents' preferences. For certain matching procedures we derive the expected revenue of the platform as a function of prices, providing insights into optimal pricing. For instance, when preferences are uncorrelated, platforms should not price discriminate on the basis of the relative sizes of the two sides of the market; this result contrasts the idea of charging more to the long side of the market when there are network effects. When preferences are positively correlated, the platform typically charges more to the short side of an otherwise symmetric market. Additionally, we show that a pairwise-stability constraint is asymptotically (in market size) costless to the platform.

ABSTRACT. This talk has been cancelled.

ABSTRACT. We introduce a sequential non-revelation mechanism for many-to-many matching markets with contracts, where hospital make take-it-or-leave-it offers to doctors. The mechanism weakly implements the set of weak-setwise stable allocations in subgame perfect Nash equilibrium when hospitals have substitutable preferences and doctors have unilateral substitutable preferences. Thus, non-revelation mechanisms constitute a valid alternative to centralized revelation mechanisms. The set of equilibria of the game is a lattice which reflects, within equilibrium outcomes, an opposition of interests between the two side of the markets. The analysis also reveals a first mover advantage absent in the model without contracts.

ABSTRACT. An agent's preference revelation obviously acts as input to a direct revelation mechanism. When such revelations are sequential, however, one agent's revelation may also act as a signal (to agents who have not yet reported) about his private information on all agents' types. Under certain conditions, an agent could even have a strict disincentive to truthfully report preferences even though outcomes are computed using a strategy-proof social choice function. We show that, under an independent-priors assumption, when a strategy-proof scf also satisfies a type of non-bossiness condition (satisfied by many but not all commonly analyzed such scf's), its sequential-mechanism counterpart preserves the robustness properties of strategy-proof direct revelation mechanisms that motivate their use in various market design settings. On the other hand, we show by example that these properties can fail to hold when preferences are correlated.

ABSTRACT. We study markets in which each agent is endowed with multiple units of an indivisible and agent-specific good. Monetary compensations are not possible. An outcome of a market is given by a circulation which consists of a balanced exchange of goods. Agents only have (responsive) preferences over the bundles they receive. We prove that for general capacity configurations there is no circulation rule that satisfies individual rationality, Pareto-efficiency, and strategy-proofness. We characterize the capacity configurations for which the three properties are compatible, and show that in this case the Circulation Top Trading Cycle (cTTC) rule is the unique rule that satisfies all three properties. We explore the incentive and efficiency properties of the cTTC rule for general capacity configurations and provide a characterization of the rule for lexicographic preferences. Finally we consider serial rules to restore Pareto-efficency and Segmented Trading Cycle Rules to restore strategy-proofness.

ABSTRACT. The paper studies a stochastic game among individuals who are struggling to survive. If productivity in a society is low, then the only equilibrium involves inefficiently selfish (autarkic) behavior. If productivity is sufficiently high, then there are several equilibria that realize substantial welfare gains through reciprocal behavior. Yet, no equilibrium is fully efficient. Equilibria for productive societies are distinguished by how they treat the wealth distribution. While conservative societies preserve the distribution, egalitarian behavior further improves welfare by transfers. Yet, both conservative and egalitarian (productive) societies exclude the poorest, even though that involves a welfare loss. So, there are a social and an individual poverty trap. The first is technological, the second behavioral.

ABSTRACT. We study perfect information games in which the set of players is the set N of positive integers and player t plays at time t in N. We provide a game that admits no subgame perfect ε-equilibrium for any ε > 0 sufficiently small. Subsequently we show that an adaptation of the iterative method used in Flesch et al (2010) provides a necessary and sufficient condition for the existence of subgame perfect 0-equilibrium in pure strategies. This result implies that if the utility function of each player is upper semi-continuous, then there exists a subgame perfect 0-equilibrium in pure strategies.         

ABSTRACT. A match is a recursive zero-sum game with three possible outcomes: player 1 wins, player 2 wins or there is a draw. Play proceeds by steps from state to state. In each state players play a ``point game'' and move to the next state according to transition probabilities jointly determined by their actions. We focus on quasi-binary matches which are those whose point games also have three possible outcomes: player 1 scores the point, player 2 scores the point, or the point is drawn in which case the point game is repeated. We show that when the probability of drawing a point is uniformly less than 1, quasi-binary matches have an equilibrium. Additionally, we can assign to each state a value of a draw so that quasi-binary matches always have a stationary equilibrium in which players' strategies can be described as minimax behavior in the associated point games.

ABSTRACT. We prove the existence of a unique pure-strategy Nash equilibrium in nice games with isotone chain-concave best replies and compact strategy sets. We establish a preliminary fixpoint uniqueness argument, thus showing sufficient assumptions on the best replies of a nice game that guarantee the existence of exactly one Nash equilibrium. Then, by means of a comparative statics analysis, we examine the necessity and sufficiency of the conditions on marginal utility functions for such assumptions to be satisfied; in particular, we find necessary and sufficient conditions for the isotonicity and chain-concavity of best replies. We extend the results on Nash equilibrium uniqueness to nice games with upper unbounded strategy sets and we present “dual” results for games with isotone chain-convex best replies. A final application to Bayesian games is exhibited.

ABSTRACT. This paper develops a new existence result for pure-strategy Nash equilibrium. In short, for a two-player game with scalar action sets, existence entails that one reaction curve be increasing and continuous and the other quasi-increasing (i.e, not have any downward jumps). The latter property amounts to strategic quasi-complementarities. The paper provides a number of ancillary results of independent interest, including sufficient conditions for a quasi increasing argmax, and new sufficient conditions for uniqueness offixed points. We present the main results in a familiar Euclidean setting for maximal accessibility. Finally, some commonly used models from applied microeconomic fields illustrate the broad and elementary applicability of the results.

ABSTRACT. We show sufficient conditions for the existence of an equilibrium in pure strategies for games in which the set of strategies of each player is a finite integer interval. We define a best reply direction function and prove that an equilibrium in pure strategies existsif the best reply direction functions of each playersatisfies a condition called direction preservingness. This result implies that an equilibrium in pure strategies exists if the payoff function of each player is quasiconcave on his own strategies and any difference between each player's payoffs when strategies of the other players increase by at most one unit is less than or equal to the half of the minimum non-zero marginal payoff of the own strategy. We apply the results to integer Cournot games with differentiated markets, in which each firm chooses an integer amount of the product and the price is also determined as an integer.

ABSTRACT. Do asset prices aggregate investors' private information about the ability of financial analysts? We show that as financial analysts become reputable, the market can get trapped: Investors optimally choose to ignore their private information, and blindly follow analyst recommendations. As time goes by and recommendations accumulate, arbitrage based on the inferred ability of analysts may become profitable again. The market can thus be trapped at times and yet be able, in the long run, to sort the pundits from the quacks. However, this process is impaired when the set of assets is expanding such that new assets are traded often: in this case, the market might be trapped indefinitely.

ABSTRACT. We introduce a learning framework in which a principal seeks to determine the ability of a strategic agent. The principal assigns a test consisting of a finite sequence of questions or tasks. The test is adaptive: each question that is assigned can depend on the agent’s past performance. The probability of success on a question is jointly determined by the agent’s privately known ability and an unobserved action that he chooses to maximize the probability of passing the test. We identify a simple monotonicity condition under which the principal always employs the most (statistically) informative question in the optimal adaptive test. Conversely, whenever the condition is violated, we show that there are cases in which the principal strictly prefers to use less informative questions.

ABSTRACT. This paper studies learning when agents evaluate outcomes in comparison to a reference point. It shows that certain models of reinforcement learning lead to classes of recursive preferences.

ABSTRACT. This paper studies a multiple prize contest with reference dependent preferences a la Koszegi and Rabin (2006). The designer chooses the prize structure to maximize the total expected effort. Contestants simultaneously undertake costly efforts to win prizes. Each contestant has private information about his ability, affecting his cost-of-effort. The prediction of the model is able to align the observed behaviour in recent laboratory experiments which is hard to reconcile under the assumption of standard preferences. More specifically high-ability contestants overexert effort while low-ability contestants exert very little or no effort in comparison to predictions with standard preferences. Moreover, the optimal prize allocation in contests differs markedly in the presence of reference dependent preferences. In particular, multiple prizes can become optimal when the cost-of-effort function is linear or concave, where standard preferences predict the optimality of a single prize. Several unequal prizes might be optimal when the cost-of-effort function is convex.

ABSTRACT. I study a problem of optimal feedback provision. An agent of uncertain ability repeatedly supplies effort and a principal provides feedback on his performance. Feedback is valuable but may discourage the agent and dampen his effort. I show that a policy, optimal for the principal among all persuasion mechanisms, is coarse yet tractable. In each period, the principal only informs the agent whether her current belief on his ability is above a chosen cutoff. The agent is expected to exert effort above the cutoff and is threatened with no feedback for deviating. Depending on performance technology, optimal feedback can be provided through a tenure-track or performance standard policy. These results alert to adverse effects of increasing performance transparency in organizations and may explain some features of professional contracts.

ABSTRACT. Shared effort games model investing resources in public projects and subsequently sharing the profits. Examples of such projects range from writing for Wikipedia to all-pay auctions like contests. In thresholded equal sharing (effort) games, an effort threshold defines which contributors receive their (equal) share. Thresholds between 0 and 1 model games like paper co-authorship and shared homework, where a minimum positive contribution is required before sharing in the profits. We fully characterize the conditions for a pure equilibrium existence for two-player shared effort games with linear project value functions and find the prices of anarchy and stability. For more players, our generalized fictitious play simulations show, when a pure equilibrium exists and what its efficiency is. The results about existence and efficiency of equilibria provide the likely strategy profiles (especially as the generalized fictitious play converges there) and the socially preferred strategies to use when contributing to public projects.

ABSTRACT. How are group symbols (e.g. a flag, Muslim veil, clothing style) helpful in sustaining cooperation and social norms? We study the role of symbols in an infinitely repeated public goods game with random matching, endogenous partnership termination, limited information flows and endogenous symbol choice. We characterize an efficient segregating equilbrium, in which players only cooperate with others bearing the same symbol. In this equilibrium, players bearing a scarcer symbol face a longer expected search time to find a cooperative partner upon partnership termination, and can therefore sustain higher levels of cooperation. We compare this equilibrium to other equilibria in terms of renegotiation proofness.

ABSTRACT. A puzzling feature of conspicuous consumption, given its signaling role, is that it is not more conspicuous. For example, luxury goods often feature subtle, difficult-to-recognize branding. We analyze a model where consumers care about their reputation for wealth and social capital. In equilibrium, wealthy but poorly-connected consumers choose loud status goods, while wealthy, well-connected consumers choose subtle status goods to separate from poorly-connected consumers. The model thus explains why "old-money" types consume subtly, whereas "nouveau-riche" types consume loudly. It also addresses the stylized fact that subtly-branded status goods tend to be pricier than their loudly-branded equivalents.

ABSTRACT. When luxury purchases signal the incomes of buyers, a monopoly will deliver signals efficiently. If competitors sell counterfeit copies of luxury goods at low prices, consumers will have to buy larger quantities to transmit the same signal, which wastes resources. Entrants do maximal harm when they produce indistinguishable replicas of existing luxury goods which causes prices to fall the furthest. Pooling, where agents do not signal, can deliver a welfare improvement over the separation that occurs under classical monopoly and competition. But only a powerful monopoly that can determine which goods are marketed can enforce this outcome. Finally, there is a trade-off among the goods that can serve as income signals: the goods that signal efficiently display a large gap between between marginal cost and the price a monopoly charges, but the same goods offer the greatest rewards to counterfeiting.

ABSTRACT. We examine the interplay between a person's individual preference and the social influence others exert upon his choices. We provide a model of network relationships with conflicting preferences, where individuals are better off coordinating with those around them, but not all prefer the same action. We test our model in an experiment, varying the level of conflicting preferences between individuals and the cost structure associated to network formation. Our findings suggest that individual preferences are more salient than social influence when there exists a structure with a dominant out-group and a dominated in-group. This case leads to two undesirable outcomes: network segregation and social inefficiency. If, however, the dominant structure of the population is relaxed, integration is achievable under conditions of low conflict. This leads to denser and efficient networks.

ABSTRACT. We consider a model of influence with a set of non-strategic agents and two strategic agents. The non-strategic agents have initial opinions, are linked through a connected network and update their opinions as in the DeGroot model. The two strategic agents have fixed and opposed opinions. They each form a link with a non-strategic agent in order to influence the average opinion in the network. This procedure defines a zero-sum game whose players are the strategic agents and their strategies are the non-strategic agents. We focus on the existence and characterization of pure strategy equilibria. The characterization of equilibrium emphasizes the influenceability of target agents and their centrality characterized by a new notion that we call intermediacy. If the strategic agents have the same impact, symmetric equilibria emerge as natural solutions. If the impacts are uneven, the high-impact agent focuses on central targets and the low-impact agent on influenceable ones.

ABSTRACT. We investigate the cases when the Bonacich measures of strongly connected directed bipartite networks can be interpreted as a Nash equilibrium of a non-cooperative game. One such case is a two-person game such that the utility functions are bilinear, the matrices of these bilinear forms represent the network, and strategies have norm at most one. Another example is a two-person game with quadratic utility functions. A third example is an m + n person game with quadratic utilitity functions, where the matrices representing the network have dimension m × n. For connected directed bipartite networks we show that the Bonacich measures are unique and give a recursion formula for the computation of the measures. The Bonacich measures of such networks can be interpreted as a subgame perfect equilibrium path of an extensive form game with almost perfect information.

ABSTRACT. If players have ambiguous beliefs about the state in global games, rational behavior depends on ambiguity not only about the state but also about others’ behavior. The impact of ambiguity is most evident when one of the actions yields a constant payoff, which we call a safe action. Ambiguous information makes more players choose a safe action, whereas low-quality information makes more players choose an ex ante best response to the uniform belief over the opponents’ actions. If the safe action and the ex ante best response coincide, sufficiently ambiguous information generates a unique equilibrium, whereas sufficiently low-quality information generates multiple equilibria. In any case, the two types of information have opposite effects. In applications to financial crises, we demonstrate that news of more ambiguous quality triggers a liquidity crisis, whereas news of less ambiguous quality triggers a currency crisis.

ABSTRACT. We study the financial crisis model, where both banking and currency crises are correlated by the connection of two markets. Depart from classical financial crises models, we allow strategic complementarity not only within a group and but also in the two different sectors like Goldstein (2005). We also accommodate the situation where agents face ambiguous information about the underling fundamental value. Under the model, we explore how degree of noise, risk (i.e., the variance of information about the fundamental value) and ambiguity, affects the possibility of the crises. We characterize when more/less risky and ambiguous information can reduce the possibility of correlated crises. Moreover, in the small limit of noise, when two crises are perfectly correlated we show that correlated crises can be prevented by manipulating the degree of risk and ambiguity. As a result, some policy implications to stabilize the economy can be drawn.

ABSTRACT. Risk-neutral sellers can extract high profits from risk-loving buyers with lotteries. To limit risk-taking, gambling is heavily regulated in most countries. I show that protecting risk-loving buyers is essentially impossible.

Even if buyers are risk-loving only asymptotically, the seller can construct a non-random winner-pays auction that ensures unbounded profits. The profits are unbounded even if the seller cannot use any mechanism that resembles a lottery. Asymptotically risk-loving preferences are both sufficient and necessary for unbounded profits.

ABSTRACT. We introduce a novel framework for modeling bounded reasoning in dynamic games, based on the idea that at each history of the game each player pays attention to some - not necessarily all - histories. We refer to this phenomenon as local reasoning, and we show that several types of bounded rationality can be studied within this framework, such as limited memory or limited foresight. We study a standard form of reasoning within our framework, according to which each player tries to rationalize her opponents' past actions at the histories that she reasons about. As a result we obtain a generalized solution concept, called local common strong belief in rationality. We characterize the strategy profiles that can be rationally played under our concept by means of a simple iterative elimination procedure. Finally, we show that standard solution concepts are special cases of rationality and local common strong belief in rationality.

ABSTRACT. Do individuals rationally choose the solution concept for a dynamic game or is their mode of reasoning a type-like predisposition? We show that an individual’s propensity to forwardly or backwardly induct is a function of (i) her belief whether the opponent’s action was a trembling hand mistake or a rational choice, and (ii) her personality traits. In a two-stage dynamic game, the individual observes an action of a computerized opponent whose hand can tremble (stage 1) before both interact (stage 2). The opponent’s action in stage 1 discloses with some probability the opponent’s belief about the individual’s choice in stage 2. The individual can either believe that (i) the opponent trembled in stage 1, or that (ii) the opponent made a rational choice. The individual consistently responds to this belief if she solves stage 2 by backwards induction in the first, and by forward induction in the second case.

ABSTRACT. Meier (2012) gave a mathematical logic foundation of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an infinitary language is used for the beliefs.

In this paper we propose an epistemic model to fix this inconsistency. We show that in the proposed model the universal knowledge-belief space exists, is complete and includes all belief hierarchies.

Moreover, by examples we demonstrate that in our model the players can agree to disagree -- the main result of Aumann (1976) does not hold --, and the conditions of Aumann and Brandenburger (1995) are not sufficient for Nash equilibrium. However, we show that if we substitute self-evidence (Osborne and Rubinstein, 1994) for common knowledge then we get at that both Aumann's and Aumann and Brandenburger's results hold.

ABSTRACT. In this paper we introduce a weaker version of the balanced contribution property by Myerson(1980), and explore the class of solutions characterized by the axiom. Our new axiom, the balanced contribution property for equal contributors, states the if two players' contributions to the grand coalition are the same, then their contributions to each other's payoffs are the same. We prove that this axiom, together with efficiency and weak strategic invariance, characterizes the class of r-egalitarian Shapley values. This class includes the egalitarian Shapley values (Joosten(1960)) and the generalized solidarity values (Casajus and Huettner (2014)) as special cases. We also provide a non-cooperative implementation of the solution.

ABSTRACT. Pillage games (Jordan in J Econ Theory 131.1:26–44, 2006, “Pillage and property”) are cooperative games which allow externalities between coalitions, and resources to contribute both to coalitions’ power and to their utility. Thus, they are well suited to modeling unstructured power contests. To this point, the pillage games literature has been entirely theoretical, partly due to a pervasive symmetry assumption that agents’ intrinsic contributions to coalitional power is identical – a property unlikely to hold in applications. This paper exhaustively analyses an asymmetric three-agent pillage game related to the characteristic function form majority game. It finds that only eight configurations are possible for the core, which contains at most six allocations. For each core configuration, the stable set is either unique or fails to exist. Only one stable set contains an allocation in the interior of the allocation simplex, a degenerate symmetric case already known in the literature.

ABSTRACT. In the current approach we consider claims problems with indivisible goods. Specifically, by applying the recursive procedures proposed by Gimenez- Gomez and Marco-Gil (2014) and Gimenez-Gomez and Peris (2014), we ensure the fulllment of order preservation and balancedness, considered by many authors as minimal requirements of fairness. Moreover, we retrieve the discrete constrained equal losses and the discrete constrained equal awards rules (Herrero and Martnez, 2008). Finally, by the recursive imposition of a lower bound and an upper bound, we obtain the average between them.

ABSTRACT. We analyze the duration of large economic declines and provide a game-theoretic model of delayed recovery. Based on this model, we show that uncertain post-recovery incomes lead to a commitment problem which limits the possibility of cooperation in ethnically heterogeneous countries. We furthermore show theoretically that strong constraints on the executive solve this problem by reducing the uncertainty associated with cooperative behavior. We test the model using standard data on linguistic heterogeneity and detailed data on ethnic power configurations. Our findings support the key theoretical prediction: stronger constraints on the political executive shorten economic declines. The effect is large in ethnically heterogeneous countries but virtually non-existent in homogeneous societies.

ABSTRACT. Being inclusive benefits not only a country but also its ruler. Why so many regimes are exclusive instead? This paper distinguishes between the distributions of current power and expected capability to master future contingencies to study the inclusiveness of ruling coalition. The subgame perfect equilibrium (SPE) shows that (1)only groups whose ratio of current power and perceived capability to master future contingencies takes medium values will be included in the coalition; (2) when treason by member groups is feasible, the admissible interval for coalition member groups diminishes significantly; (3)if repressing rebelion preserves net gain for the incumbent power leader, the ruling coalition has various levels of inclusiveness; and (4)it is more inclusive if the incumbent power leader has a large power margin over that of other groups.

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ABSTRACT. In this study, we formulate positive and negative externalities caused by changes in the supply of shared vehicles as ride sharing games. The study aims to understand the price of anarchy (PoA) and its improvement via a coordination technique in ride sharing games. A critical question is whether ride sharing games exhibit a pure Nash equilibrium (pNE) since the PoA bound assumes it. Our result shows a sufficient condition for a ride sharing game to have a finite improvement property and a pNE similar to potential games. This is the first step to analyze PoA bound and its improvement by coordination in ride sharing games. We also show an example of coordinating players in ride sharing games using signaling and evaluate the improvement in the PoA.

ABSTRACT. We consider the problem of designing distribution rules to share ‘welfare’ (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., (weighted) Shapley values; however, a characterization of the space of distribution rules that guarantee the existence of a Nash equilibrium is unknown. Our work provides an exact characterization of this space for a specific class of scalable and separable games. Given arbitrary local welfare functions W, we prove that a distribution rule guarantees equilibrium existence for all games if and only if it is equivalent to a generalized weighted Shapley value on some ‘ground’ welfare functions W', which can be distinct from W. Accordingly, in order to guarantee equilibrium existence in all games with any fixed local welfare functions, it is necessary to work within the class of potential games.

ABSTRACT. We consider an infinite game, in which productive coalitions interact repeatedly over time. We characterize both, the terms of trade and the endogenous cooperation structure in this game when just three general axioms are satisfied: (1) the coalition structure formed is consistent with agents’ payoff expectations; (2) each coalition that forms distributes the entire surplus among its members; (3) in any coalition, all agents are treated symmetrically relative to their payoff expectations. Assuming the game ends after each date with a vanishing probability, we obtain unique shares and a unique cooperation structure that satisfy these conditions. In an application, we show how, in a complete network, a unique price arises and agents specialize in either buying or selling while, in an incomplete network, transactions occur, generally, at multiple prices and some agents become arbitrageurs that buy and sell at different prices.

ABSTRACT. A standard result from the game theoretic literature on international environmental agreements is that coalitions are either "broad but shallow" or "narrow but deep". Hence, the stable coalition size is small when the potential welfare gains are large. We modify a standard climate coalition game by adding a - seemingly - small but realistic feature: we allow countries to delay climate negotiations until the next "round" if a coalition forms but decides to remain inactive. It turns out that results are surprisingly different under this modification. In particular, a large coalition with deep emissions cuts forms if countries are sufficiently patient. Our results also indicate that countries should try hard to overcome coordination problems in the formation of a coalition. A more cooperative outcome may then be reached, and it may be reached more quickly.

ABSTRACT. A major threat on human well-being is the accelerated rate of ecosystem degradation. Restoration of degraded ecosystems entails cooperation among multiple agents such as land owners, agencies and sometimes countries. These agents may have incentives to contribute less (free-ride), which may lead to inefficient or incomplete treatment. Here we introduce a dynamic game approach to study how to restore ecosystems by multiple agents, taking into account the costs of both treatment and degradation over time. We assume no enforcement mechanisms and no binding agreements. We show that, under certain conditions, there exists a solution (subgame perfect Nash equilibrium) where all agents actively participate, albeit slowly enough, and no agent has an incentive to free-ride. This Nash equilibrium may coexist with an inefficient Nash equilibrium dictating no contribution by any agent. This implies that certain restoration projects may not require external investment as managers may self-organize to resolve their conflicts.