ABSTRACT. We study the simplest form of two-sided markets: one seller, one buyer and a single item for sale. It is well known that there is no fully-efficient mechanism for this problem that maintains a balanced budget. We characterize the quality of the most efficient mechanisms that are budget balanced, and design simple and robust mechanisms with these properties. We also show that even minimal use of statistical data can yield good results. Finally, we demonstrate how a mechanism for this simple bilateral-trade problem can be used as a ``black-box'' for constructing mechanisms in more general environments.

ABSTRACT. Procurement regulation aimed at curbing discrimination in auctions requires that all bidders are treated equally. However, Deb and Pai (2013) show that such regulation poses virtually no restriction on the ability to discriminate. We propose a simple rule - imitation perfection - that restricts discrimination in a meaningful way. With homogeneous bidders, imitation perfection implies that in every equilibrium conditional on their valuation all bidders earn the same surplus. There exist revenue and social-surplus-optimal auctions that are consistent with imitation perfection. With heterogeneous bidders, imitation perfection is incompatible with revenue and social-surplus optimization. Thus, there exists a trade-off between non-discrimination and optimality.

ABSTRACT. We consider a moral hazard issue inherent in the equity auctions of assets such as oil & gas leases and corporate takeovers. After the auction, the winning bidder decides whether or not to make follow-up investments in the acquired asset and makes the equity payment out of the revenue from it according to the auction outcome. Before the auction, the seller holds private information about the possible returns on that investment and must decide whether to disclose it. Disclosing her private information causes moral hazard in different degrees to bidders with different productivities. In contrast to the seminal linkage principle by Milgrom and Weber (1982), expected seller revenues may be higher when she does not disclose her private information than when she commits to publicly announcing it regardless of whether it is good or bad.

ABSTRACT. This paper provides a general characterization of subgame-perfect equilibria for a strategic timing problem, where two firms have the (real) option to invest irreversibly in some market. Profit streams are uncertain and depend on the market structure. The analysis of the problem emphasizes its dynamic nature and exploits only its economic structure. In particular, the determination of equilibria with preemption is reduced to solving a single class of constrained stopping problems. The general results are applied to typical state-space models from the literature, to point out common deficits in equilibrium arguments and to suggest alternative equilibria that are Pareto improvements.

ABSTRACT. This paper examines conjectures, open-loop equilibrium and Markov perfect equilibrium in dynamic differentiated duopoly games. We explore relationships between open-loop equilibrium and Markov perfect equilibrium in both a model of quantity adjustment and that of price adjustment. Open-loop equilibrium in a quantity adjustment model corresponds to static Cournot equilibrium when time goes to infinity. Open-loop equilibrium in a price adjustment model corresponds to static Bertrand equilibrium when time goes to infinity. Conjectural variations for both the dynamic model of quantity adjustment and that of price adjustment are identified. We also show that Markov perfect equilibrium in a quantity adjustment model is more competitive than static Cournot equilibrium.

ABSTRACT. In this paper we analyse a dynamic game modelling Cournot oligopoly with sticky prices. We calculate Nash equilibria: feedback and open loop, and compare resulting trajectories of price and production. Although our paper is not the first such model of oligopoly, it appears to be the first paper in which non-stationary open loop Nash equilibria were rigorously calculated. Therefore, our analysis allows us to study and compare closed loop and open loop Nash equilibria which are not constant. We prove that feedback equilibrium production from some time instant on, is strictly greater than the open loop equilibrium production, with reverse inequality for prices. We also analyse behaviour of equilibrium price and production as functions of parameters of the model and we obtain, among others, that the feedback equilibrium steady states do not converge to static Cournot equilibrium as the speed of adjustment tends to infinity, unlike the open loop equilibrium.

ABSTRACT. Behavioral contract theory typically argues that agents who differ in their intrinsic motivations to collaborate or to compete would be screened by principals, or self-sort in labor market competition. This view is in contrast with the empirical observation that workers' perceived support from coworkers is a key factor for labor turnover. The present study considers a principal-multiple agents model with independent observable efforts. Agents are privately informed about their more or less pronounced altruistic (spiteful) preferences. It is shown that the interim-efficient labor contract is a pooling contract that ex interim Pareto-dominates any allocation that could be achieved under complete information. Hence, all parties involved prefer the composition of social types at work to be random. The distributive effects of interim-efficient contracting are closely related to the hawk-dove game, with the principal taking the role of nature. Interim-efficient contracting implies relative or team performance pay in a payoff-equivalent way.

ABSTRACT. A principal decides whether or not or to take an action on each of a number of agents without the use of transfers. Each agent desires the action to be taken and has private information (his type) about the principal’s payoff from taking the action on him. The principal’s payoff exhibits complementarities across agents, which the principal leverages by coordinating the agents. Coordination involves taking the action on agents with high (low) types more often when the other agents also have high (low) types. Due to complementarities, coordination optimally accepts failure when the consequence are small in order to ensure success when the gain is high. We also and that, in a variety of environments, the action is taken more often for an ex-ante inferior agent, a phenomenon we call favoritism. One possible application of our setting is a firm downsizing a division and deciding which employees to keep.

ABSTRACT. This paper models the use of statistical hypothesis testing in regulatory approval. A privately informed agent proposes an innovation. Its approval is beneficial to the proponent, but potentially detrimental to the regulator. The proponent can conduct a costly clinical trial to persuade the regulator. I show that the regulator can screen out all ex-ante undesirable proponents by committing to approval based on a simple statistical test. Its level is the ratio of the trial cost to the proponent’s benefit from approval. In application to new drug approval, this level is around 15% for the average Phase III clinical trial.

ABSTRACT. I consider a model in which a firm invests in both product quality and a costly signaling technology, and the firm's reputation is the market's belief that its quality is high. Signaling influences the rate at which consumers’ receive information about quality: the firm can either promote, which increases the arrival rate of signals, or censor, which decreases the arrival rate of signals. I study how the firm's incentives to build quality and signal depend on its reputation. The firm's ability to control information dramatically changes incentives. Promotion and investment in quality are complements: the firm has stronger incentives to build quality when the promotion level is high. Costly promotion can reduce the firm's incentive to build quality; this effect persists even as the cost of building quality approaches zero. Censorship and investment in quality are substitutes. The ability to censor can destroy a firm's incentives to invest in quality.

ABSTRACT. I analyze a twice-repeated trust game in which an Investor chooses in each period whether to invest or not in a project carried out by an Entrepreneur who may not be reliable. The value of the project is fixed through time and is either common knowledge, or private knowledge of the Entrepreneur. The Investor learns about the reliability of the Entrepreneur by observing whether he repays investments or not. If the project is valuable enough, an unreliable Entrepreneur invests in reputation in order to obtain financing also in the second round. There is shown to always exist parameter environments under which ex-ante welfare is maximized for each player if the Entrepreneur is privately informed about the value of his project.

ABSTRACT. We analyze how reputation concerns of a decision-maker affect her ability to extract information from reputation-concerned advisors. Contrary to most of the literature, we show that the decision-maker's concerns for her reputation as an expert can improve information aggregation. When the decision-maker's reputation concerns are very low, she is tempted to ask for advice regardless of her private information, which undermines advisors' truth-telling incentives. Very high reputation concerns destroy the incentives to seek advice. The optimal strength of the reputation concerns maximizes advice-asking without undermining advisors' incentives. Prior uncertainty about the state of nature calls for a more reputation-concerned decision-maker, unless the uncertainty becomes too high, in which case the reputation concerns become (almost) irrelevant. The expected competence of advisors has a similar effect. A higher number of advisors generally results in higher optimal reputation concerns of the decision-maker.

ABSTRACT. We consider the problem of allocating sets of objects to agents and collecting payments. Each agent has a preferences over the set of pairs consisting of a set of　objects and a payment. Preferences can be non-quasi-linear. Non-quasi-linear preferences describe environments where the wealth effect is non-negligible. We investigate the existence of efficient and strategy-proof rules. A preference relation is unit-demand if given a payment level, for each set of objects, the most preferred one in the set is at least as good as the set itself; it is multi-demand if given a payment level, when an agent receives an object, receiving some additional object(s) makes him better off. We show that if a domain contains all the unit-demand preferences and at least one multi-demand preference relation, and if there are more agents than objects, no rule satisfies efficiency, strategy-proofness, individual rationality, and no subsidy for losers on the domain.

ABSTRACT. We demonstrate the abundance of asymmetric equilibria in a standard marriage market model, when agents must only engage in heterosexual marriage: agents of different gender are not guaranteed to have the same payoff even under equal opportunities, even if all other factors, such as own type or the distribution of partner types, are same across genders. Then we allow for same-sex marriage, and we demonstrate that under equal opportunities, only symmetric equilibria survive.

ABSTRACT. We consider an assignment market with one seller who owns several indivisible heterogeneous goods and many buyers each willing to buy up to a given capacity. In this market, the core contains the allocation in which every buyer gets his marginal contribution to the grand coalition. We characterize the minimum and the maximum competitive equilibrium prices to determine when the buyers- optimal and the seller-optimal core allocations are competitive. In addition, we characterize in terms of the valuation matrix the coincidence between the core and the set of competitive equilibrium payoff vectors.

ABSTRACT. The decision making mechanism at university is one of important factors affecting university's performance. We look for appropriate mechanisms in the case when clear criteria for effectiveness are missing and at the same time one can rely on professors' knowledge. We study the situation when the university's founder has to delegate decision making power and choose among several types of governance. The first type of governance is sharing governance, in this case the decision is made on the basis of majority voting. The second type is autocratic governance without rotation. The third type is autocratic governance with rotation, and finally we have governance when the decisions are made by a committee. If the founder cannot assess the preferences of professors and choose professors with specific characteristics, sharing governance gives the best results. The second best chose is to delegate the decision to a committee.

ABSTRACT. In this paper we ask how do colleges differentiate themselves, and what is the impact of this differentiation on the structure and efficiency of higher education markets. We propose a model that draws on both the horizontal and vertical differentiation literature.

The benefit to Students attending college depends on their ability and the academic standard of the college. The extent of the mismatch between a student's ability and the college they attend is analogous to a transport cost. However, because higher ability students are willing to pay more than lower ability students, colleges are also vertically differentiated. We also explain why the cost of travel function must be non-monotonic in match distance.

We present a number of welfare results that help explain some features of higher education markets. We also highlight similarities and differences between the results of our hybrid model and those of Hotelling and Thisse.

ABSTRACT. This paper studies reassignment problems in matching markets where there exists some initial matching. In this context, a natural Individual Rationality (IR) constraint emerges : agents must obtain a weakly better match than their initial one. In the standard college admission problem, it is well known that the standard Deferred Acceptance mechanism is the unique Pareto-efficient (for both sides), fair and strategy-proof mechanism. In the reassignment problem however, it is known that this mechanism fails to be IR. Both in the literature and in practice (e.g. to assign teachers in France) a simple modification of this mechanism has been proposed to ensure IR and keep strategy-proofness. However, we show that this modification is not Pareto-Efficient. We then show that there is a unique IR, Pareto-efficient and strategy-proof mechanism. Then using data on the assignment of teachers in France, we show that the gains of this new mechanism are important.

ABSTRACT. It is well known that the set of mixed equilibrium payoffs of any finite n-player game is a nonempty semialgebraic and compact subset of R^n. We show that for n>2 the converse is true: any nonempty semialgebraic and compact subset of R^n is the set of equilibrium payoffs of some finite n-player game. The proof is constructive. We also show that this implies that some problems concerning finite games are undecidable.

ABSTRACT. In finite games, the graph of the Nash equilibrium correspondence is a semialgebraic set (i.e. it is defined by finitely many polynomial inequalities). This fact implies many game theoretical results about the structure of equilibria. We show that many of these results can be readily exported to Poisson games even if the expected utility functions are not polynomials. We do this proving that, in Poisson games, the graph of the Nash equilibrium correspondence is a globaly subanalytic set. Many of the properties of semialgebraic sets follow from a set of axioms that the collection of globaly subanalytic sets also satisfy. Hence, we easily show that every Poisson game has finitely many connected components and that at least one of them contains a stable set of equilibria. By the same reasoning, we also show how generic determinacy results in finite games can be extended to Poisson games.

ABSTRACT. We extend Sonnenschein's and Tian's theorems for existence of a maximal element of a discontinuous preference to more general discontinuous preferences when the space of outcomes are not necessarily Hausdorff or convex. We apply our condition to obtain necessary and sufficient ordinal conditions for existence of coalitional equilibria in discontinuous games. Our approach allows to unify several Nash equilibrium existence results and most notably those of Reny, Bay-Tian-Zhou, and Barelli-Meneghel.

ABSTRACT. We characterize voting procedures according to the solution that they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(with a unanimously disliked candidate, the majority-preferred among the other two is elected). In the larger class of direct mechanism scoring rules, Approval Voting is characterized by a single axiom – it is majoritarian after eliminating a Pareto dominated candidate (MEPD)(with a Pareto-dominated candidate, the majority-preferred among the other two is elected). However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity.

ABSTRACT. D'Apresmont Gerard-Varet (AGV) mechanism implements efficient social choice in a budget-balanced manner, however it is susceptible to a joint misreport by a coalition of agents, and it may have inefficient equilibria. This paper extends AGV mechanism by putting more structure on its monetary transfers, making all equilibria efficient and coalition-proof. In the resulting direct mechanism each agent is paid the Shapley value generated from the expected externalities his report imposes on others. This makes each group of agents to be paid in total the expected externality their report imposes on others, and makes it Bayesian incentive compatible to report truthfully. Moreover, any agent can guarantee to receive his ex ante efficient payoff if he always reports truthfully, making all equilibria efficient. It is generically impossible to make truthful report a dominant strategy for all coalitions.

ABSTRACT. Convergence rate and stability of a solution concept are classically measured in terms of ``eventually'' and ``forever'', respectively. In the wake of recent computational criticisms to this approach, we study whether these time frames can be updated to have states computed ``quickly'' and stable for ``long enough''.

Logit dynamics allows irrationality in players' behavior, and may take time exponential in the number of players $n$ to converge to a stable state (i.e., a certain distribution over pure strategy profiles). We prove that any potential game, for which the behavior of the logit dynamics is not chaotic as $n$ increases, admits distributions stable for a super-polynomial number of steps in $n$ no matter the players' irrationality, and the starting profile of the dynamics. The convergence rate to these \emph{metastable distributions} is polynomial in $n$ when the players are not too rational. Our proofs build upon a number of involved technical contributions.

ABSTRACT. We present attractiveness, a refinement criterion on the defining mathematical properties of three evolutionary equilibrium concepts, i.e., the evolutionarily stable strategy, the evolutionarily stable equilibrium and the truly evolutionarily stable state. We call an evolutionary equilibrium meta-stable if it is dynamically, structurally as well as conceptually stable for a non-singleton class of dynamics. We show that any attractive evolutionary equilibrium is (a) dynamically stable, i.e., if the system at equilibrium is slightly disturbed, it will return to equilibrium, (b) structurally stable, i.e., preserves defining properties for small perturbations of the underlying structure of the system, (c) conceptually stable, i.e., equivalent to at least one other attractive evolutionary equilibrium, for non-singleton classes of dynamics. We also show that each strict saturated (Nash) equilibrium is meta-stable for a vast class of evolutionary dynamics.

ABSTRACT. We establish a sample path large deviation principle for sequences of Markov chains arising in game theory and other applications. As the state spaces of these Markov chains are discrete grids in the simplex, our analysis must account for the fact that the processes run on a set with a boundary. A key step in the analysis establishes joint continuity properties of the state-dependent Cramer transform, the running cost appearing in the large deviation principle rate function.

ABSTRACT. I study the optimal contract offered by a principal funding a financially constrained agent to work on a multistage project. The project requires all stages to be completed to yield benefits. Exerting effort in early stages is informative but not conclusive about the feasibility of future stages. The optimal contract features milestones to be achieved before a deadline. If the project is ultimately successful, the agent is rewarded with a share of the benefits that depends on performance in all stages. The timing of successes in early stages influences the beliefs in later stages and the deadlines and shares. Later successes imply more pessimism about the project's quality. The effect of learning does not necessarily induce deadlines and shares to be monotone in success time. First, later successes induce more pessimism about the project. Second, more pessimism makes incentive provision harder. For late successes the second effect outweighs the first.

ABSTRACT. This paper studies whether and how strategy revision opportunities affect levels of collusion in indefinitely repeated two-player games. Consistent with standard theory, we find that such opportunities do not affect strategy choices, or collusion levels, if the game is of strategic substitutes. In contrast, there is a strong and positive effect for games of strategic complements. Revision opportunities lead to more collusion. The latter cannot be explained by renegotiation or standard risk-dominance considerations, but is consistent with a notion of fear of miscoordination based on minmax regret.

ABSTRACT. We study optimal contest design when two asymmetric players compete in a complete-information all-pay-auction contest with multi-dimensional favoritism. The favoritism can take the form of a player being given a head-start advantage ("additive bias"), or an effectiveness advantage which enhances each unit of effort("multiplicative bias") expended by a player. We solve for the optimal contest for a designer who would like to achieve each of the following objectives: maximizing the total effort, maximizing the total score, maximizing the highest effort by a single player, and maximizing the winner’s effort. We …find that a "fairness condition" is necessary under each of the four objectives of the designer, which is also robust to non-linear forms of favoritism. Our findings contribute to a better understanding of the optimal unfair contests, and generalize some of the results in the previous literature with just one-dimensional unfairness.

ABSTRACT. This paper examines the emergence of nonpracticing entities in the market for patents. While patent trolls monetize their patents through the threat of litigation against alleged infringers, intermediaries instead intend to protect their affiliated firms by buying patents that would otherwise fall in trolls’ hands. We develop a model of patent acquisition through an auction incorporating both trolls and intermediaries. We find that firms can never win the auction when individually competing against the troll, while the seller’s revenue sharply increases in response to the troll’s participation in the auction. We then introduce an intermediary in the model. Since the patent is collectively financed through voluntary contributions, firms tend to free ride on other contributors. While the intermediary’s probability to outbid the troll in the auction is positive, the collective action issue inherent to his funding mechanism greatly hampers his performance in the auction and undermines the seller’s revenue.

ABSTRACT. We enrich the Crawford and Sobel (1982) model of strategic communication between an informed sender and an uninformed receiver by adding repeated interactions and voluntary transfer payments. Transfers play two roles here: they incentivise decision-making and signal information. Although full separation can be ‘frictionlessly’ attained in equilibrium, partial or complete pooling is optimal if preferences are sufficiently divergent. In this case, extreme information is optimally pooled to discipline the receiver’s decision-making by reducing her reneging temptation. As an extension, we consider a partially-informed receiver. As the receiver becomes more informed, welfare strictly decreases because self-enforcing agreements become harder to sustain.

ABSTRACT. We consider a Sender-Receiver Game in which the Sender can send either a costless cheap-talk message or a costly verifiable message. While the Sender has private information about the state of the world, the Receiver chooses an action, which yields to a specific utility for both players. Since the preferences about the actions may differ, depending on the state of the world, the Receiver may or may not trust the messages if they are not verified. In a discrete setting we show under which conditions full revelation is possible and also describe the players optimal behaviour if full revelation is impossible. We also state necessary and sufficient conditions for fully revealing equilibria in a continuous model. In both models we distinguish between equilibria where just one type of message is sent and where the Sender chooses the type of message depending on the state of the world.

ABSTRACT. This paper studies equilibrium selection in persuasion games where the receiver's actions are binary, and discusses how to justify the most informative equilibrium as a reasonable consequence. In general, there exist multiple equilibria in this environment even if the sender's private information is fully certifiable, and the convention of focusing on the most informative equilibrium is followed without formal justification. However, we show that the existing selection criteria in the literature on strategic communication hardly justifies such a convention; in particular, these criteria might select the least informative equilibrium. We then suggest the notion of certifiable dominance, and show that the most informative equilibrium is uniquely selected by a perfect Bayesian equilibrium constructed using certifiably undominated strategies. This criterion could also uniquely select the most informative equilibrium when the sender's private information is partially certifiable.

ABSTRACT. This paper analyzes the impact of local and global interactions on individuals’ action choices. Players are located in a network and interact with each other with perfect knowledge of their neighborhood and probabilistic knowledge of the complete network topology. Each player chooses an action, from some finite set, which imposes an externality on their neighbors as well as an externality on the complete network. Players deal with two opposing forces: they obtain utility from sharing their choices with their neighbors (positive local externality) but suffer disutility from sharing the same choice with all members of the network (negative global externality). We find the conditions for the existence of all symmetric Bayesian Nash equilibria and translate them to a characterization in terms of the main properties of the network topology. The balance between local satisfaction and global dissatisfaction (congestion) partially explains the equilibrium outcome.

ABSTRACT. We study the application of taxes to a network-routing game, and we assume that the tax-designer knows neither the network topology nor the tax-sensitivities and demands of the agents. We show that it is possible to design taxes that guarantee that selfish network flows are arbitrarily close to optimal flows, despite the fact that agents’ tax-sensitivities are unknown to us. These taxes enforce optimal behavior in any routing game without a priori knowledge of the specific game parameters. In general, these taxes may be very high; accordingly, for affine-cost parallel-network routing games, we explicitly derive the optimal bounded tolls and the best-possible performance guarantee as a function of a toll upper-bound. Finally, we restrict attention to very simple fixed-toll methodologies and show that they are incapable of providing strong performance guarantees if the designer lacks good information about either the network topology or the user sensitivities.

ABSTRACT. In this study we investigate a version of the Inspection Game first introduced by Dresher (1962), where the inspector may use a mixture of partial and full inspections. With a partial or incomplete inspection, a violation may only be found with a probability significantly less than one. We investigate the behaviour of players in the equilibrium and describe some of its qualitative features. We show that as long as the opportunity for a full inspection exists, the inspector never starts his sequential inspections with a partial inspection. As the game has been modelled as a zero sum game, by investigating the value of the game we have an efficient tool to compare the efficiency of the full and partial inspections.

ABSTRACT. This paper studies a concept of proportional use of force in a counter-terrorism action. The terrorist organization decides whether to attack or not to attack the state, while the state decides about his counter-terrorist measure. The state is supposed not to use a 'non-proportional' force, namely, the counter-terrorist measure taken by the state should be sufficient to remove a threat imposed by terrorists, but not higher than that. The level of force required against the terrorist organization is a private information of the organization. The model predicts under which conditions terrorists will not attack the state, and under which conditions with a positive probability the attack will take place, the state will react with a tough counter-terrorist measure and the state may be accused for non-proportional use of violence.

ABSTRACT. In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen from a specified set. We show that it is NP-hard for the designer to make these choices optimally, even in zero-sum games. In fact, it is already intractable to decide whether a given action is (potentially or necessarily) played in equilibrium. We also consider incompletely specified symmetric games in which all completions are required to be symmetric. Here, hardness holds even in weak tournament games and in tournament games. The latter result settles the complexity of the possible and necessary winner problems for a social-choice-theoretic solution concept known as the bipartisan set. We finally give a mixed-integer linear programming formulation for weak tournament games and evaluate it experimentally

ABSTRACT. We present a complete method with the best-known upper bound for computing an epsilon-Nash equilibrium in multiplayer games. The main components of our tree-search-based method are a node-selection strategy, an exclusion oracle, and a subdivision scheme. The node-selection strategy determines the next region to be explored. The exclusion oracle provides a provably correct sufficient condition for there not to exist an equilibrium in the region. The subdivision scheme determines how the region is split if it cannot be excluded. Unlike well-known incomplete methods, our method does not need to proceed locally, which avoids it getting stuck in a local minimum that may be far from any actual equilibrium. The run time of our algorithm grows rapidly with game size; this suggests a hybrid scheme where one of the relatively fast prior incomplete algorithms is run, and if it fails to find an equilibrium, then our method is used.

ABSTRACT. In this paper, we propose two kinds of analytic relationships between the Shapley value and the configuration value. Firstly, by introducing an appropriate probability distribution on the coalition configuration set, we prove that the Shapley value coincides with the expectation of the configuration values. Then, as a corollary, we establish that the Shapley value equals the average of the configuration values over each set of the same kind of coalition configurations. The equivalence of these two results is ensured by proving that the corollary implies the first result. Finally, we show that similar analytic relationships also hold between the Shapley value and the dual configuration value, while they do not hold between the Banzhaf-Coleman index and the generalized Banzhaf-Coleman index.

ABSTRACT. We present a noncooperative game model of coalitional bargaining, closely based on that of Gul (1989) but solvable by backward induction. In this game, Gul’s condition of 'value additivity' does not suffice to ensure the presence of a subgame perfect Nash equilibrium that supports the Shapley value, but a related condition - 'no positive value externalities' - does. Multiple equilibria can arise only in the event of ties, and with a mild restriction on tie-break rules these equilibria all support the Shapley value.

ABSTRACT. We suggest a foundation of the Shapley value via the decomposition of solutions for cooperative games with transferable utility. A decomposer of a solution is another solution that splits the former into a direct part and an indirect part. While the direct part (the decomposer) measures a player's contribution in a game as such, the indirect part indicates how she affects the other players' direct contributions by leaving the game. The Shapley value turns out to be unique decomposable decomposer of the naïve solution, which assigns to any player the difference between the worth of the grand coalition and its worth after this player left the game.

ABSTRACT. In last four decades, party polarization and income inequality have been rising in tandem. In this paper we try to build a link between them. We consider a Spatial model of redistribution with heterogeneity in voters' wealth. Two ex ante identical candidates for a public office compete by proposing redistributive taxes. Voters also care about candidates’valence, which is determined by individual contributions. Voters contribute to their preferred candidates to persuade other voters who initially prefer the other candidate. Rich voters have the strongest preferences for tax rates and are more likely to contribute. In equilibrium, policy polarization (divergence) depends on income inequality. With low enough inequality, median voter theorem holds; otherwise, there exist polarized equilibria in which one party chooses a policy that appeals to a large share of poor voters, while another party will select a policy that is preferred by a smaller group of rich voters.

ABSTRACT. This paper analyzes candidate incentives in a spatial model of common-value elections - in essence synthesizing the very different but canonical approaches of Condorcet and Downs. Office motivation can push candidates toward the political center, but the welfare consequences of this are opposite those of standard private-value models. Moreover, in large elections, a candidate who believes that truth is on her side sees no need to moderate, and may thus remain highly polarized even if she is highly office motivated.

ABSTRACT. This paper considers the normative foundation of government based on a Hobbesian anarchy where one region may pillage the other. A center that takes enough power from the regions and helps the victim to fight the aggressor can deter warfare thereby incentivizing productive efforts of the regions, but with less power the regions become less productive. This paper characterizes the social-surplus maximizing allocation of power, which depending on the parameters can be fully decentralized to the regions or centralized to some degree. The paper proves that, when the marginal product of power and the supermodularity between power and efforts are sufficiently small, every fully decentralized system generates less social surplus at equilibrium than some centralized one. In a numerical example, every fully decentralized system generates less social surplus than even the total centralization, with regions completely powerless and the center maximizing the tax revenues extracted from them.

ABSTRACT. We introduce a theory of ranking sets of accomplishments in the presence of objectively incomparable marginal contributions (apples and oranges). Our theory recommends benchmarking, a method under which an individual is deemed more accomplished than another if and only if she has achieved more benchmarks, or important accomplishments. We show that benchmark rules are characterized by four axioms: transitivity, monotonicity, incomparability of marginal gains, and incomparability of marginal losses. The latter two properties are local, and hence we endogenously derive a concept of a global, objective good, which we call a benchmark.

ABSTRACT. We study binary, sequential voting procedures in settings where several privately informed agents have single-peaked preferences on a finite set of alternatives. We identify two intuitive conditions on binary voting trees, convexity of divisions and monotonicity of qualified majorities, ensuring that sincere voting at each stage forms an ex-post perfect equilibrium in the associated extensive form game with incomplete information. We illustrate our findings with several case studies.

ABSTRACT. We consider the aggregation of agents’ von Neumann-Morgenstern’s utility functions into a societal von Neumann-Morgenstern utility function. We start from Harsanyi’s (1955) axiomatization of utilitarianism, and ask when a social preference order that satisfies Harsanyi’s axiom uniquely reveals society’s marginal rates of substitution between the probabilities of any two agents’ most preferred alternatives. We then introduce three axioms for these revealed marginal rates of substitution. Our main result is that the only welfare function satisfying these three axioms is the relative utilitarian welfare function. This welfare function, that was introduced in Dhillon (1998) and Dhillon and Mertens (1999), normalizes agents’ utility functions so that the lowest utility is 0 and the highest is 1, and then adds up the utility functions. The three axioms that we introduce are related to axioms that Dhillon and Mertens used, but our axioms allow a simpler and more transparent derivation of the main result.

ABSTRACT. I study the attribution of responsibility to agents for the implementation of an event, when the event's implementation depends on the interaction of multiple agents and/or chance. In particular, I develop a notion of causal responsibility, which is based on a counterfactual-reasoning approach, incorporate the notion into a framework of responsibility preferences, study its implication for the allocation of punishment and reward in a game-theoretic environment, and test the predictions of the theory with existing experimental evidence. Responsibility preferences imply that, in addition to their preferences over monetary payoffs, agents have a taste to reward (punish) other agents for the implementation of what they judge as good (bad) events, to the extent that those agents are causally responsible for the event.

ABSTRACT. We study the prevalence of belief free strategies in repeated games with stochastic private monitoring. In these games players receive noisy private signals of their opponent's action each period, and with some probability each period they also view the entire history of play without noise. The opponent is not informed when the noiseless history is revealed, so the game is one of private monitoring. In an experiment we ask subjects to choose their next period's action after observing the noisy signal. The subject then discovers whether they learn the entire (noiseless) history of play. If they do, they have the opportunity to revise their next-period action. Subjects using belief-free strategies will not revise their next-period action after observing the entire history.

ABSTRACT. Bayesian updating remains the benchmark for dynamic modeling under uncertainty. Recent theory and evidence suggests individuals process information in a biased manner when it relates to personal characteristics or future life outcomes. Specifically, updating has been found to be asymmetric, with good news receiving more weight than bad news. I put this theory and evidence to the test, by examining information processing across multiple domains with varying stake conditions. I do not find that good news is over-weighted relative to bad news, but in fact, I find the opposite asymmetry. However the same updating patterns are present in domains that have no scope for the type of psychological bias discussed in the literature. As in previous research, I also find gender differences in updating behavior, however these differences are similarly present across domains. Despite deviations from the mechanics of Bayes' rule, posterior beliefs are well approximated by Bayesian posteriors.

ABSTRACT. A market with only one seller and many buyers is considered. The seller owns several indivisible heterogeneous objects on sale and each buyer can acquire many objects. Buyers have submodular valuation functions over the set of all packages of objects. The aim of this paper is to analyze the following mechanism. Simultaneously, each buyer requests a package by announcing how much he would pay for it. After all buyers' requests, the seller decides the final assignment of packages and the prices. If a buyer gets a package of objects, it must be his request or an allocation at least as good as his request. The subgame perfect equilibrium outcomes of the mechanism correspond to the Vickrey outcome (see Vickrey, 1961) of the market.

ABSTRACT. We extend the partnership dissolution model by Cramton et al. (CGK, 1987) and allow for differences in willingness to accept (WTA) and willingness to pay (WTP). We determine a necessary and sufficient condition for the existence of an individually rational, ex post efficient, budget balanced and incentive compatible dissolution mechanism for the prominent 50-50 ownership case. In contrast to CGK no partnership can be dissolved ex-post efficiently if a partner’s difference between WTA and WTP is within a certain range. Consequently, partners might not be willing to participate in the widely analyzed k+1-price auction. For k=1/2 we study a k+1-price auction with voluntary participation and compare its performance with a k+1-price auction which allows separate bids for different shares. Only for small differences in WTA and WTP the first outperforms the second in terms of efficiency and ex ante expected utilities.

ABSTRACT. This paper studies an auction that maximizes the expected social surplus under an upper-bound constraint for the seller's expected revenue (revenue cap). Such a constrained-efficient auction may arise, for example, when the auction designer is "pro-buyer", i.e., he maximizes the weighted sum of the buyers' and the seller's payoffs in auctions, where the weight for the buyers is larger than that for the seller. We characterize the constrained-efficient auction mechanisms, and obtain their important properties under reasonable assumptions. First, the seller sets no reserve price, and sells the good for sure. Second, with a nontrivial revenue cap, "bunching" is necessary (i.e., failure of the pointwise maximization approach). Finally, with a sufficiently severe revenue cap, bunching occurs (at least) "at the top" (i.e., failure of "no distortion at the top"), which is implemented by a bid cap.

ABSTRACT. We study workers' incentives for reporting problems within a firm, by considering an OLG organization consisting of an apprentice and a manager. The apprentice is responsible for detecting and reporting a problem, and the manager is responsible for solving the reported problem. An unsolved problem may cause accidents, in which case, the blame is placed on the manager if the problem has been reported in the past. The apprentice has an incentive to conceal a problem since if he reports it but the manager's ability is too low for the problem, the responsibility is transferred to the apprentice since he becomes a manager in the next period. We show that concealment is more likely when the problem gets larger over time. We also show that if the blame to the manager for ignoring a problem gets large, concealment may get worse.

ABSTRACT. We examine the strategic use of Corporate Social Responsibility (CSR) in oligopolistic markets. In our two-stage model, the level of CSR determines the weight that a firm puts on consumer surplus in its objective function before it decides upon supply. First, we consider symmetric Cournot competition and show that the endogenous level of CSR is positive for any given number of active firms. However, positive CSR levels imply smaller equilibrium profits. Second, we find that an incumbent monopolist may profitably use CSR as an entry deterrent. Both results indicate that CSR may increase market concentration and possibly be anticompetitive. We identify circumstances in which CSR mitigates the problem of excessive entry and increases total welfare but decreases consumer surplus.

ABSTRACT. In 2014, the EU passed a directive on antitrust damages actions which facilitates the compensation of cartel victims. Anti-trust infringers are liable jointly and severally: a victim can sue any cartelist and this firm must pay compensation on behalf of all. The sued cartelist can later seek redress from its former collaborators. The directive requires that individual compensation contributions reflect relative responsibility but leaves open how to quantify this. We propose to invoke the Shapley value for assessing cartelists' contributions to equilibrium price increases. We provide first structural results and address two practical questions: are there useful bounds on fair damage shares? Does any simple heuristic, like equating responsibility with market shares, approximate the Shapley allocation better than others?

ABSTRACT. This talk has been cancelled.

ABSTRACT. We study a rating system in which a set of individuals (e.g., the customers of a restaurant) evaluate a given service (e.g, the restaurant), with their aggregated opinion determining the probability of all individuals to use the service and thus its generated revenue. We explicitly model the influence relation by a social network, with individuals being influenced by the evaluation of their trusted peers. On top of that we allow a malicious service provider (e.g., the restaurant owner) to bribe some individuals, i.e., to invest a part of his or her expected income to modify their opinion, therefore influencing his or her final gain. We analyse the effect of bribing strategies under various constraints, and we show under what conditions the system is bribery-proof, i.e., no bribing strategy yields a strictly positive expected gain to the service provider.

ABSTRACT. We consider a multi-sided assignment game with the following characteristics: (a) the agents are organized in m sectors that are connected by a graph G* associated with a weighted m-partite graph G on the set of agents, (b) a basic coalition is formed by agents from different sectors that are connected by G* and (c) the worth of a basic coalition is the addition of the worths of all its pairs that belong to connected sectors. We provide a sufficient condition on the weights to guarantee balancedness of the related multi-sided assignment game. Moreover, when the graph G* is a tree, we prove the game is strongly balanced and the core is described by means of the cores of the underlying two-sided assignment games associated with the edges of G. If the tree G* is a star, then the core can be characterized by means of the competitive prices.

ABSTRACT. Gale and Shapley [D. Gale and L. S. Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, 69(1):9–15, 1962] have shown that in marriage markets, where men and women have preferences over potential partners of the other gender, a stable matching always exists. In this paper, we study a more general framework with d different genders due to Knuth [D. E. Knuth. Mariages stables. Les Presses de l’Université de Montréal, 1976]. The genders are ordered in a directed cycle and agents only have preferences over agents of the subsequent gender. Agents are then matched into families, which contain exactly one agent of each gender. We show that there always exists a stable matching if there are at most d+1 agents per gender, thereby generalizing and extending previous results. The proof is constructive and computationally efficient.

ABSTRACT. We test for the competitive consequences of women’s preference for men who have higher incomes than themselves. We show that the key characteristic of this “reference dependent preference” (RDP) is to escalate the competition women face as their incomes increase by reducing the pool of men they desire while simultaneously expanding the pool of other women who desire those men. Consequently, high-income women can be made worse off when high-income men are even richer or more plentiful, because either increases the returns to poorer women in competing for those men. We exploit variations in local sex ratios and men’s incomes across major cities in China to test for changes in the online dating search intensity, marriage probability, and household bargaining power of women. As predicted, the search intensity, singles probability, and share of housework of only the high-income women increase with the incomes and availability of men.

ABSTRACT. Citation indices measure and rank publication records of scholars. Some well known indices reward records that balance impact I with productivity P; many publications with few citations will score poorly, as will a small number of heavily cited papers. Often implicit, however, is a single optimal trade-off ratio r of productivity to impact -- think of r as a fixed scale factor relating the unit size on the I axis to that on the P axis. Scholars, or entire disciplines, may be assigned higher index values if their publication records “fit” better with r; this can scramble the relative ordering of scholars within a discipline, in an undesirable way. We propose four scale-invariant indices modeled loosely on John Nash’s bargaining solution. These preserve some degree of impact-productivity balance, while adjusting r to best fit the publication record of each scholar. We mention the advantages, and discuss axioms that capture scale-invariance.

ABSTRACT. We propose a new index of individual scientific productivity that formally accounts for coauthorship. In contrast to existing measures, our index, CoScore, reflects the complete coauthorship network, not only the publication record of the author being ranked. CoScore uses the varying levels of success of all academic partnerships to infer, simultaneously, an author's productivity and her credit for each of her papers. Crucially, the productivities of all authors are determined endogenously via the solution of a fixed point problem. We illustrate CoScore for a large database of papers in economics.

ABSTRACT. This note axiomatically justifies a simple scoring rule for multiple-choice tests. The rule permits choosing any number, k, of available options and grants 1/k-th of the maximum score if one of the chosen options is correct, and zero otherwise. This rule satisfies a few desirable properties: simplicity of implementation, non-negative scores, discouragement of random guessing, and rewards for partial answers. This is a novel rule that has not been discussed or empirically tested in the literature.

ABSTRACT. A plausible incentive compatibility requirement based on behavioral considerations, is that agents only consider manipulations that are ``close'' to their true preference. In a finite voting environment, this is interpreted as preference orderings that are at a Kemeny distance of one from the true preference ordering. A social choice function (SCF) is adjacent manipulation (AM) proof, if it is immune to such manipulations. A domain satisfies equivalence if every AM-proof SCF defined on this domain, is also strategy-proof. Sato (2013) provides a necessary condition and a separate, stronger sufficient condition for equivalence. We extend Sato's results in several directions. We identify a condition which is necessary for equivalence; in conjunction with Sato's necessary condition, it is sufficient for equivalence for SCF's satisfying unanimity. We also provide an additional, stronger sufficient condition for equivalence without unanimity. We show that every unanimous and AM-proof SCF is also group strategy-proof provided equivalence holds.

ABSTRACT. Schummer (Journal of Economic Theory, 2000) introduced the concept of bribeproof mechanism, which, in a context where monetary transfer between agents is possible, requires that manipulations through bribes are ruled out. Unfortunately, in many domains, the only bribeproof mechanisms are the trivial ones which return a fixed outcome.

This work presents one of the few constructions of non-trivial bribeproof mechanisms for the quasi-linear environments. Though the suggested construction applies to rather restricted domains, the results obtained are tight: For several natural problems, the method yields the only possible bribeproof mechanism and no such mechanism is possible on more general domains.

ABSTRACT. This study proposes a double implementation of two solution concepts derived from minimax and maximax strategies and examines its relationship with strategy-proofness (or dominant strategy implementation). Although the combination of the two solution concepts is strictly weaker than a dominant strategy, their double implementation implies strategy-proofness when the preference domain satisfies a richness condition; consequently, their double implementation is almost equivalent to a dominant strategy implementation. Our richness condition is weaker than the condition of Sato (2013) for adjacent strategy-proofness to be equivalent to strategy-proofness, and is satisfied by the general domains based on convexity, including standard economic environments and single-peaked preferences allowing weak orders.

ABSTRACT. In this paper we consider the robustness of subgame-perfect implementation in situations when the preferences of players are almost perfectly known. More precisely we consider a class of information perturbations where in each state of the world players know their own preferences with certainty and receive almost perfectly informative signals about the preferences of other players. We show that implementations using two-stage sequential move mechanisms are always robust under this class of restricted perturbations, while those using more stages are often not.

ABSTRACT. This paper considers a dynamic process of n-person social choice problems under q-majority where a status-quo policy is challenged by an opposing policy drawn randomly in each period. The opposing policy becomes the next status-quo if it receives at least q votes. We characterize stochastically stable policies under a boundedly rational choice rule of voters. Under the best response rule with mutations, a Condorcet winner is stochastically stable for all q-quota rules, and uniquely so if q is greater than the minmax quota. Under the logit choice rule, the Borda winner is stochastically stable under the unanimity rule. Our evolutionary approach provides a dynamic foundation of the mini-max policies in multidimensional choice problems with Euclidean preferences.

ABSTRACT. We study the evolutionary dynamics of a discrete-time continuous-opinion model under bounded confidence in a complete network with random meetings when different types of agents are present, i.e. regular, stubborn and insincere. We find the following. Even though the decision-making succumbs to the contraction principle, the opinion dynamics converges to multiple opinion clusters if regular agents are present with insufficient threshold levels. Further, we identify the conditions under which the process with stubborn agents generates long-run consensus, permanent disagreement or permanent fluctuation in opinions. Even a small deviation towards the inconsistent behavior by a small fraction of agents may turn the society into a persistent fluctuation in opinions. The size of a quorum reduces the effects of insincere counterparts. Simulations generated some non-linearities in the process of opinion formation, giving us some additional insights into the relationship between agents' tolerance and the level of extremism in a society.

ABSTRACT. In this paper we study the long run convention emerging from stag-hunt interactions when errors occur at a rate that is inversely related to the payoff previously earned, i.e., condition-dependent mistakes. We find that, if interactions are sufficiently stable over time, then the payoff-dominant convention emerges in the long run. Instead, if interactions are volatile, then the safer convention emerges even if it is not risk-dominant. We contrast the results under condition-dependent mistakes with results under alternative error models: error rates that are constant over states, i.e., uniform mistakes, and error rates that depend on expected losses, i.e., payoff-dependent mistakes.

ABSTRACT. Research on the advantage of sexual over asexual reproduction is widely spread. Many hypotheses try to explain effects that compensate the disadvantages of the (expensive) sexual way of reproduction. In our work, we focus on the differences in the genetics of the species with respect to their reproduction method. Based on theoretical work by Edhan et al. [2015], we developed a software tool that tracks the growth of species depending on the chosen way of reproduction. In order to verify the theoretical results, we are able to adjust lots of initial settings like for example the available genotype space or the survival chance of arising genotypes. Besides examining the effects in genotype space, we also examine what happens in allele space. We use our software to investigate various scenarios like mutations or spatial structures that are difficult to examine theoretically.

ABSTRACT. 'Why sex' has long been a puzzle. The randomness of sexual recombination, which potentially lowers fitness, contradicts expectations of monotonic fitness landscape climbing. We show that sex implements a machine learning no-regret algorithm that is a goal-directed walk through genotype space. The algorithm reliably works even though each generation is a tiny sample of the vast genotype space. Simulations indicate this gives sex an evolutionary advantage, even in stable, unchanging environments. Asexual populations rapidly reach a fitness plateau, but the learning aspect of the no-regret algorithm most often eventually boosts the fitness of sexual populations past the maximal viability of corresponding asexual populations. The randomness of sexual recombination, rather than a hindrance, is a crucial component of the learning by sampling no-regret algorithm.

ABSTRACT. Predicting the behavior of human participants in strategic settings is an important problem in many domains. Most existing work either assumes that participants are perfectly rational, or attempts to directly model each participant's cognitive processes based on insights from cognitive psychology and experimental economics. In this work, we present an alternative, a deep learning approach that automatically performs cognitive modeling without relying on such expert knowledge. We introduce a novel architecture that allows a single network to generalize across different input and output dimensions by using matrix units rather than scalar units, and show that its performance reaches that of the previous state of the art, which relies on expert-constructed features.

ABSTRACT. The zero-determinant (ZD) strategies, raised by Press and Dyson, can enforce a linear relationship between a pair of players' scores in the iterated Prisoner's Dilemma. In particular, the Extortionate ZD strategies can enforce and exploit cooperation and provide a player with a score advantage, and consequently, higher scores than those from either mutual cooperation or Generous ZD strategies. In a set of laboratory experiments, we demonstrate that both the Generous and the Extortionate ZD strategies indeed enforce a unilateral control of the reward. When the experimental setting is sufficiently long and the computerized nature of the opponent is known to human subjects, the Extortionate strategy outperforms the Generous strategy. Human subjects' cooperation rates when playing against Extortionate and Generous ZD strategy are similar after learning has occurred. We observe that more than half of the Extortionate strategists finally obtain an average score higher than that from mutual cooperation.

ABSTRACT. This paper experimentally examines repeated prisoners’ dilemma with random termination, where monitoring is imperfect and private. Our estimation of individual strategies indicates that a significant proportion of our subjects follow generous tit-for-tat strategies. However, their retaliation policies are systematically inconsistent with the standard-theoretical predictions implied by the generous tit-for-tat equilibria. Contrary to the theory, our subjects tend to retaliate more in the high accuracy treatment than in the low accuracy treatment. They also tend to retaliate more than the standard theory predicts in the high accuracy treatment, while they tend to retaliate lesser in the low accuracy treatment. In order to describe our experimental results as equilibrium behavior, we demonstrate an alternative theory from the behavioral viewpoint, which permits players to be motivated by not only pure self-interest but also naïveté and reciprocity.

ABSTRACT. An advisory committee with common values and asymmetric information provides a recommendation to a decision maker facing a binary choice. We investigate the effect of a transparency requirement---making committee members' actions observable---on the committee’s ability to influence the decision maker. We show that unless the preferences of the committee and decision maker are very close, requiring transparency is harmful, as it destroys the committee's ability to provide any useful information. In contrast, if committee members are able to verifiably reveal their signals then transparency can be beneficial.

ABSTRACT. We study the effect of the arrival of exogenous news in dynamic games of Bayesian persuasion. A receiver chooses what action to take, and when to act. If Receiver waits, exogenous news may be observed. A sender chooses a first information structure that generates a signal before the news and, if Receiver waits, a second signal structure after the news. Receiver observes the signal structures, as well as the corresponding signal realized. We show that, in the sense of Blackwell, information provided by Sender before the news is non-monotonic in the quantity of exogenous news. For very small and very large quantities of exogenous news, Sender provides enough information for Receiver to act before the news with probability one. By contrast, for intermediate quantities of exogenous news, Sender curbs the information she provides, in a way that minimizes the chances of Receiver acting early against Sender’s interest.

ABSTRACT. We study the efficiency of price cap regulation in a competitive market with congestion externalities. Each link in a network is owned by a profit-maximizing firm that sets a price for travel. The subgame perfect equilibrium of the associated game is called oligopoly equilibrium in Acemoglu and Ozdaglar (2007). The latency costs of an oligopoly equilibrium can be arbitrary worse than the optimal latency costs. Therefore we consider competition regulation in the form of a price cap. On the one hand, setting a price cap of zero corresponds to a Wardrop equilibrium. On the other hand, setting a price cap of infinity corresponds to an oligopoly equilibrium. We characterize a tight bound of $8/7$ between the latency costs at the optimal price cap and the optimal latency costs, when there are two links with affine latency functions. In general, this ratio is unbounded due to the non-existence of oligopoly equilibria.

ABSTRACT. In "The curse of simultaneity", Paes Leme at al. show that there are interesting classes of games for which sequential decision making and subgame perfect equilibria avoid worst case Nash equilibria, resulting in substantial improvements for the price of anarchy. This is called the sequential price of anarchy. A handful of papers have lately analyzed it for various problems, yet one of the most interesting open problems was to pin down its value for linear atomic routing games, where the price of anarchy equals 5/2. The main contribution of this paper is the surprising result that the sequential price of anarchy is unbounded even for linear symmetric routing games, thereby showing that sequentiality can be arbitrarily worse than simultaneity for this class of games. Additionally, we prove price of anarchy bounds and, that in these games, even with two players, computing the outcome of a subgame perfect equilibrium is NP-hard.

ABSTRACT. Non-linear probability weighting is an integral part of descriptive theories of choice under risk such as prospect theory. But why do these objective errors in information processing exist? Should we try to help individuals overcome their mistake of overweighting small and underweighting large probabilities? In this paper, we argue that probability weighting can be seen as a compensation for preexisting biases in evaluating payoffs. In particular, inverse S-shaped probability weighting in prospect theory is a flipside of S-shaped payoff valuation. Probability distortions may thus have survived as a second-best solution to a fitness maximization problem, and it can be counter-productive to correct them while keeping the value function unchanged.

ABSTRACT. In many situations of decision-making under uncertainty, the set of possible states of the world and the set of possible outcomes each have a topological structure, and the only feasible acts are those where the outcome varies continuously with the state. Indeed, in some situations, the only feasible acts are differentiable functions. Savage’s (1954) axioms do not apply to such a restricted domain of acts. Nevertheless, we axiomatically characterize a Subjective Expected Utility (SEU) representation of ex ante preferences in this environment. Our SEU representation involves a unique Borel probability measure on the state space, and an essentially unique, continuous utility function on the outcome space.

ABSTRACT. We investigate a framework for non-cooperative games in normal form where players have behavioral preferences following Prospect Theory (PT) or Cumulative Prospect Theory (CPT). On theoretical grounds CPT is usually considered to be the superior model, since it normally does not violate rst order stochastic dominance in lottery choices. We find, however, that CPT when applied to games may select purely dominated strategies, while PT does not. For both models we also characterize the cases where mixed dominated strategies are preserved and where violations may occur.

ABSTRACT. We consider a framework where each player has incomplete preferences and is viewed as a multiutility decision-maker. We define a decision rule as a probability distribution over each player's set of infinitely many utilities and prove first that, in a basic model of incomplete information with linear utilities, the decision rule corresponds to the utilitarian aggregation one. Consequently, we establish a generalization of Harsanyi's (1955) famous possibility result for infinitely many individuals (Theorems 1-2). Finally, we prove the existence of a Nash equilibrium for normal form games with incomplete information where players are multiutility decision-makers and conform with the utilitarian decision rule (Theorem 3).

ABSTRACT. A key challenge in solving extensive-form games is dealing with large, or even infinite, action spaces. In games of imperfect information, the leading approach is to find an equilibrium in an abstraction that includes only a few actions at each decision point. However, it is difficult to know which actions the abstraction should include without first solving the game, and it is infeasible to solve the game without first abstracting.

We introduce an algorithm that combines abstraction with equilibrium finding by enabling actions to be added to the abstraction at run time. It can quickly add actions while provably not having to restart equilibrium finding. It enables anytime convergence to a Nash equilibrium of the full game. Experimentally it outperforms fixed abstractions at every stage: early on it improves as quickly as equilibrium finding in coarse abstractions, and later converges to a better solution than equilibrium finding in fine-grained abstractions.

ABSTRACT. Perfect equilibrium (or trembling-hand perfect equilibrium) is a refinement of Nash equilibrium for finite n-person games. For any extensive-form game with perfect recall, the literature shows that a perfect equilibrium of its agent normal-form representation is also a perfect equilibrium of the extensive-form game itself, which always results in a sequential equilibrium. To effectively determine such a perfect equilibrium, this paper develops a smooth path-following method. The method closely approximates Nash equilibria of perturbed games by incorporating a logarithmic barrier term into each player's payoff function with an appropriate combination. It is proved that there exists a smooth path which starts from a totally mixed strategy profile and ends at a perfect equilibrium. A predictor-corrector method is adopted for numerically following the path. Numerical results further confirm the effectiveness of the method.

ABSTRACT. This talk will be given on Sunday, July 24, 11:30 in session Sun11-K on learning.

The session Thu11-R: sports on Thursday, July 28, will start at 11:30.

ABSTRACT. The rules of many sports are not fair—they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all five penalty kicks, gives a substantial advantage to the first-kicking team, both in theory and practice. We show that a so-called Catch-Up Rule for determining the order of kicking would not only make the shootout fairer but also is essentially strategyproof. By contrast, the so-called Standard Rule now used for the tiebreaker in tennis is fair. We briefly consider several other sports, all of which involve scoring a sufficient number of points to win, and show how they could benefit from certain rule changes, which would be straightforward to implement.

ABSTRACT. AAny political leader must be judged by her supporters and this is a constraint that is more or less binding depending on the authoritarian system. The literature on autocracies has notanalyzed the fact that policies have multiple dimensions and that people observe the effects of some policy dimensions with noises. Our objective is to study the effects of these differences in public perception on the dictator's accountability. The crucial innovation is the two dimensional policy. Our model produces three clear results: the region of the selectorate's de facto power such that reciprocal accountability works shrinks as opacity increases, counter intuitively both the probability of full efficient and full inefficient policies decrease as opacity increases, finally, and mostly interesting, the expected probability of a coup might have a non monotone behavior wrt opacity, so that at intermediate level an increment in opacity might actually increase the likelihood of a coup.

ABSTRACT. We study the feasibility and efficiency of policy reforms in polarized democracies. We develop an election model where (i) reforms are costly and these costs increase with the extent of policy change, and (ii) politicians differ in their ability to carry out reforms efficiently. We identify a so-called Reform Dilemma, which manifests itself in two variants. First, from a static perspective, low-reform-ability politicians may be elected, who impose high costs on citizens for each reform step. Second, from a dynamic perspective, incumbents may choose socially undesirable policies to align the social need for reform with their own reform ability, thereby increasing re-election chances or securing re-election outright. In general, both manifestations of the Reform Dilemma are more pronounced when political parties' positions are polarized. Furthermore, the Reform Dilemma is independent of the exact point in time when the abilities of candidates reveal themselves and become common knowledge.

ABSTRACT. We identify a novel channel through which increased competition among information providers decreases the efficiency of electoral outcomes. A number of profit-maximizing firms compete to sell information to a group of Bayesian agents about how two political candidates compare on several issues. Voters can disagree on which issues are important to them (agenda) and on how each issue in their agenda should be addressed (slant). We show that competition forces firms to differentiate the type of information they produce. In particular, differentiation leads to higher provision of information on issues where there is higher disagreement in the electorate. Although voters become individually better informed, the share of votes going to the socially optimal candidate decreases. We also show that this inefficiency is magnified if there is higher polarization in the underlying preferences of the society.

ABSTRACT. Feasible elimination procedures (Peleg, 1978) play a central role in constructing social choice functions which have the following property: in the associated game form, for any preference profile there exists a strong Nash equilibrium resulting in the sincere outcome. In this paper we provide an axiomatic characterization of the social choice correspondence resulting from applying feasible elimination procedures. The axioms are anonymity, Maskin monotonicity, and independent blocking.

ABSTRACT. This paper investigates the robustness of aggregation rules to strategic manipulation. Preferences over alternatives are extended to preferences over orders, called hyper-preferences. An individual manipulates an aggregation rule at some profile if misrepresenting one's preference induces a social ordering that is preferred to the current one according to the hyper-preference generated by said preference. We provide a set of necessary and sufficient conditions on aggregation rules so that there exist hyper-preferences for which no individual can manipulate the outcome. Moreover, we introduce a constraint for domains of hyper-preferences that allow for non-trivial and non-manipulable aggregation rules. Later on, we shift our focus to hyper-preferences which satisfy the betweenness criterion. We provide a complete study of strategy-proofness for pairwise unanimous and anonymous aggregation rules defined for 3 alternatives. Finally, we show that when there are at least 3 alternatives, pairwise unanimity, anonymity, reverse orders independence and strategy-proofness are mutually incompatible.

ABSTRACT. This paper implements the citizen-candidate paradigm in a laboratory experiment to investigate candidate behavior under different electoral rules and for varying costs of running for office. Comparing the candidates’ observed entry decisions under plurality voting and proportional representation (PR) I find support for the theoretical predictions. Entry rates are significantly higher under PR when such a treatment effect is expected but not in the absence of a predicted difference. This suggests that the increase in entry found under PR is not due to a heuristic but a response to the change in incentives. Furthermore, I find that as theoretically predicted higher costs of running for office lead to fewer entrants that are more centrist. Additionally, I replicate the well-known finding of over-entry compared to the Nash equilibrium predictions.

ABSTRACT. This paper introduces an endogenous cognitive hierarchy model in which players are assumed to best-reply holding heterogeneous beliefs on the other players' cognitive levels. Contrary to the previous models, players are allowed to consider presence of opponents at their own cognitive level. This extension is shown to eradicate the incompatibility of standard cognitive hierarchy models in the games where the best-reply function is an expansion mapping. We employ the model to explain asymptotic voting behavior in information aggregation problems of the Condorcet Jury Theorem. Behavioral assumption of the strategic thinking turns out to be a crucial factor in whether the asymptotic efficiency is obtained or not. We conducted laboratory experiments and obtained evidences that the endogenous cognitive hierarchy model provides significant improvements upon standard cognitive hierarchy models and symmetric Bayesian Nash equilibrium in explaining observed behavior of voters.

ABSTRACT. In this experiment, subjects play both roles of a modified version of the trust game (Berg et al. 1995) and state their beliefs about their opponents’ behavior in both roles. We investigate how people’s trust and trustworthiness are connected to their beliefs about their opponents. Our results confirm that most people carry out their actions based on their beliefs of what the others would do in their positions. Moreover, subjects’ behavior as trustees are significantly influenced by their experience and feedback of playing the trustors role. The experience of playing the trustees role, even without feedback information, helps the trustors make a better prediction of the trustees’ behavior. People are not as consistent in the trustee role.

ABSTRACT. In a zero-sum stochastic game, two players interact repeatedly, and receive a stream of payoffs that depends on their actions and on a variable called state of nature. The state of nature may change along the game, according to players' actions. The first model of this kind was introduced by Shapley (1953). A widely studied question is to determine whether the value of the n-stage game and the value of the lambda-discounted game converge as n goes to infinity and the discount factor lambda goes to 0. This question was studied in an extremely large variety of models, according to the information and the state dynamics structure, both in discrete time and continuous time. This talk starts with an overview of the topic, illustrating its theoretical significance and its connections with other problems in economics, computer science and pure mathematics. One model that has received particular interest is the model of discrete-time zero-sum stochastic games with signals. Mertens (1986) conjectured that the limit value should always exist in this model. In the second part of the talk, we give a counterexample to this conjecture. Indeed, we consider the particular class of stochastic games with public signals on the state and perfect monitoring, and provide an example that does not have a limit value.