ABSTRACT. In many settings, bidders may differ in their information sources or ability to utilize a good. We model a common-value second-price auction in which bidders are given both a signal and a type and investigate equilibrium in multidimensional auctions. Our first result proves the existence of symmetric equilibrium when types are multidimensional. We also find sufficient conditions for equilibrium to by unique and strictly increasing. We then look at the impact of disclosing information about opposing bidders. We consider models where type corresponds to the precision of the signal or a private-value advantage. In both of these settings, publicly disclosing all bidder's types decreases revenue compared to when types are private knowledge. Simple examples show that this decrease can be very large. Our finding suggests a practical and easily implementable information design recommendation which can restore stability to revenue of the auction.

ABSTRACT. I solve a first price auction for bidders with asymmetrically distributed budget constraints and public valuations. I fully characterize the set of equilibria for this framework. I analyze the effect of asymmetry in the budget distributions on equilibrium bidding behavior and implications for the auctioneer’s revenue. If bidders are sufficiently symmetric (there exists a threshold for the reverse hazard rates of budget distributions), the degree of asymmetry in the budgets has no influence on the equilibrium strategies: bidding the entire budget is the unique equilibrium strategy. However, if asymmetry gets sufficiently severe(at least one reverse hazard rate undercuts this threshold), mass points in the equilibrium strategies arise. I derive pure strategy weakly monotonic bidding functions and show, that under mild regularity conditions, the weaker bidder bids more aggressively than his stronger opponent. Furthermore, information disclosure about budget distributions for ex-ante symmetric bidders is never profitable for the auctioneer.

ABSTRACT. We analyze a divisible good uniform-price auction with two groups with a finite number of identical bidders. When an equilibrium exists it is unique and the relative market power of a group increases with the precision of its private information and decreases with(its transaction costs. Consistent with the empirical evidence, we find that an increase in the transaction cost of a group of bidders induces a strategic response of the other group according to which they diminish their reaction to private information and submit steeper schedules. The "stronger" group (with more precision of private information, lower transaction costs and/or more oligopsonistic) has more market power and has to receive a higher subsidy to behave competitively. The deadweight loss increases with the quantity auctioned and with the degree of payoff and informational asymmetry when the strong group values the asset at least as the weak group.

ABSTRACT. We analyze symmetric, two-bidder all-pay auctions with interdependent valuations and discrete type spaces. Relaxing previous restrictions on the distribution of types and the valuation structure, we present a construction that characterizes all symmetric equilibria. We show how the search problem this construction faces can be complex. In equilibrium, randomization can take place over disjoint intervals of bids, equilibrium supports can have a rich structure, and non-monotonicity of the equilibrium may result in a positive probability of allocative inefficiency when the value of the prize is not common. Particular attention is paid to the case in which an increase in a bidder’s posterior expected value of winning the auction is likely to be accompanied by a corresponding increase for the other bidder. Such environments are "highly competitive" in the sense that the bidder’s higher valuation also signals that the other bidder has an incentive to bid aggressively.

ABSTRACT. We investigate the repeated version of Shubik's dollar auctions, in which the type of the opponent and their level of rationality is not known in advance. We formulate the problem as an adversarial multi-armed bandit, and we show that a modified version of the ELP algorithm, tailored to our setting, can achieve O(sqrt(ST)) performance loss (compared to the best fixed strategy), where S is the cardinality of the set of available strategies, and T is the number of (sequential) auctions. We also show that under some further conditions, these bound can be improved to O(S^(1/4)sqrt(T)), and O(sqrt(T)), respectively. Finally, we consider the case of spiteful players. We prove that when a non-spiteful player bids against a malicious one, the game converges in performance to a Nash equilibrium if both players apply our strategy to place their bids.

ABSTRACT. An extensive literature provides evidence for overbidding in auctions. Risk aversion, joy of winning, anticipated regret etc. do not always offer sufficient explanations. We show that the second-price all-pay auction presents a very interesting environment to study spite and overbidding. In equilibrium we should expect spiteful participants to increase their bids for small valuations and decrease their bids for high valuations. We measure spite and bidding behaviour for our participants and find that, indeed, the more spiteful participants also follow a bidding pattern which is theoretically in line with more spitefulness.

ABSTRACT. This paper contributes to the theory of recommended retail prices. We consider a model with two firms that compete by setting prices in a homogeneous product market, where firms first set a recommended price, that serves as an upper bound on the actual retail price. The key element is that a fraction of consumers are partially informed and make a purchasing decision solely on basis of the recommended price. We show that if these consumers use a simple heuristic, then recommended retail prices lead to lower retail prices on average. The effect is less strong if consumers have rational expectations.

ABSTRACT. We propose a labor market model for service and tech industries, where a firm's primary asset is its workforce. Firms attract applicants with high wages, and managers identify talent among the applicants. If talent is scarce, firm-applicant matching is positive assortative, with skilled managers posting high wages and attracting an unselected applicant pool; if talent is plentiful, matching is negative assortative, with skilled managers posting low wages and attracting an adversely selected applicant pool. In either case, negative assortative matching is efficient. We then embed this labor market model into a firm dynamics framework, and into a firm hierarchy framework. These model extensions explain persistent productivity dispersion between firms, and wage dispersion across firms and across hierarchy levels.

ABSTRACT. This talk has been cancelled.

ABSTRACT. Foreign direct investors face uncertainty about the economic and political conditions of the host country. In a two period game, we allow the host country's government to mitigate such an uncertainty by sending a signal through fiscal policy. Our main finding states that a populist government may mimic a conservative one in order to attract foreign direct investment (FDI), and this choice depends mainly on its impatience degree and the originally planned FDI stock. We highlight the role of the government's reputation in attracting foreign capital and thus provide some policy implications. Moreover, our model explains why in some countries considered populist governments adopt conservative policies in the beginning of its terms of office.

ABSTRACT. Contract enforceability in financial markets often depends on the aggregate actions of agents. For example, high default rates in credit markets can delay legal enforcement or reduce the value of collateral, incentivizing even more defaults and potentially affecting credit supply. We develop a theory of credit provision in which enforceability of individual contracts is linked to aggregate behavior. The central element behind this link is enforcement capacity, which is endogenously determined by investments in enforcement infrastructure. Our paper sheds new light on the emergence of credit crunches and the relationship between enforce- ment infrastructure, economic growth, and political economy distortions.

ABSTRACT. We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. As a policy implication, it is not necessary to process all the sensitive data simultaneously and run a centralized clearing procedure.

ABSTRACT. Standard legislative bargaining models assume that an agreed-upon allocation is final, whereas in practice, there exist mechanisms for challenging passed legislation when there is lack of sufficient consensus. Such mechanisms include popular vote requirements following insufficient majorities in the legislation. This paper analyzes a legislative bargaining game whose outcome can be challenged through a referendum. I study the effects of this institution on the bills passed in the legislature and analyze the incentives they provide for reaching grand bargains. The proposer party's trade-off between an expensive partner and a threatening opponent in the referendum summarizes the bargaining problem. The results indicate that it is possible to observe surplus coalitions formed in equilibrium even though smaller coalitions are sufficient for the passage of a bill and that measures of post-bargaining power do not necessarily translate into higher equilibrium payoffs. Moreover, disparities in campaigning resources incentivize challenge procedures.

ABSTRACT. We show the effects of the bargaining power of labour unions on product innovation under decentralised and centralised wage bargaining. In this context, we show the implications of preference function, which affects the market size. A higher union bargaining power increases innovation if bargaining is decentralised, the market expansion effect is weak and the cost of innovation is moderate but low. Otherwise, a higher union bargaining power reduces innovation. Hence, whether a higher union bargaining power increases or decreases product innovation depends on the type of wage bargaining, market expansion effect and the cost of innovation.

ABSTRACT. In a dynamic model of merger negotiation with two-sided private information two-sided endogenous initiation, this paper investigates (1) what determines the timing of M&A initiation, and (2) who initiates the M&A negotiation; (3) why bid premia are different between target-initiated deals and bidder-initiated deals. The key driving force for the results is that the timing of initiation can reveal information about the target's private signal of its stand-alone value, and the bidder's private signal about its valuation for the target's firm. The model predictions are consistent with the empirical evidence that emphasizes the role of private information in deal-initiation.

ABSTRACT. We formalize job mobility procedure through a generalized Shapley-Scarf model of markets for finitely many pure indivisible goods without money, where individuals may be married and couples simultaneously apply for jobs. Moreover, we endow the set of jobs with a geographical structure in order to capture the fact that couples wish to live together. Married individuals valuate allocations taking into account both the satisfaction they get from their job and the distance to their mate. Two concepts of Core stability are defined where blocking coalitions should involve individuals with their mate. We prove that Core existence strongly rests upon the precise way married individuals valuate matchings, as well as the properties of the initial matching and the location structure. We show that Core existence strongly rests upon the precise way married individuals valuate matchings, as well as the properties of the initial matching and the location structure.

ABSTRACT. We formulate a distributional form of the stable marriage problem for continuum economies in which matchings are joint distributions on the characteristics of girls and boys. Agents are allowed to choose from a match dependent menu of contracts that lies in a compact space. Our model accomodates both the classical marriage model and the assignment game with side-payments. Furthermore, we allow for widespread externalities that depend on statistical properties of matchings. Stable matchings exist in full generality. Every stable matching in the continuum problem is the limit of stable matchings in finite marriage problems. All matchings in distributional form can be purified to one-to-one matchings of individuals in an individualistic model.

ABSTRACT. I study the many-to-many matching problem induced by the popular dating app Tinder. I provide empirical evidence suggesting that its matching procedure is unstable, and show that its assignments can be setwise and even pairwise blocked. Any alternative stable mechanism either violates the users' privacy or has an unreasonably complex message space.

ABSTRACT. We consider land rental problems where there are several communities that can act as lessors and a single tenant who does not necessary need all the available land. A rule should determine which communities become lessors, how much land they rent and at which price. Our first result is a complete characterization of the family of rules that satisfy land monotonicity and non-manipulability under land reassignment. We also define two parametric subfamilies. The first one is characterized by adding a property of weighted standard for two-person. The second one is characterized by adding consistency and continuity.

ABSTRACT. This paper studies the question of when we can eliminate investment inefficiency in a general mechanism design model with transferable utility. We show that when agents make investments only before participating in the mechanism, inefficient investment equilibria cannot be ruled out whenever an allocatively efficient social choice function is implemented. We then allow agents to make investments before and after participating in the mechanism. When ex post investments are possible and an allocatively constrained-efficient social choice function is implemented, efficient investments are implementable in subgame-perfect equilibria if and only if the social choice function is commitment-proof (a weaker requirement than strategy-proofness). Commitment-proofness ensures the efficiency of investments by suppressing the agents’ incentives to make costly ex ante investments which may work as a commitment device. Our result implies that in the provision of public goods, subgame-perfect implementation of efficient investments and efficient allocations is possible even given a budget-balance requirement.

ABSTRACT. For the model of allocating (object) types to agents, where each type has a certain number of copies (the capacity) and each agent has a preference ranking over types and he should receive at most one copy of at most one type, we introduce a property, rank-respecting unavailable-type-invariance (rr-UTI), which requires that when the po- sitions of the unavailable types (the types which have zero capacity) are shuffled at a preference profile in such a way that the relative rank of each type among the agents’ preferences is preserved, the assignment should not change. We show that immedi- ate acceptance mechanisms are the only mechanisms satisfying resource-monotonicity, weak non-wastefulness, consistency, favoring-higher-ranks, and rr-UTI.

ABSTRACT. We analyze a new type of bandit where an agent is confronted with two-dimensional uncertainty. The agent does not know whether ability or effort is required to succeed at a given task. Moreover, the agent does not know her own ability. In each period, after deciding whether to exert effort or not, the agent observes a success or a failure and updates her beliefs about both the task and her ability accordingly. In contrast to standard bandit models, the agent gains information even when she is not exerting effort. In this setting different agents react to failure in different ways; while some agents find it optimal to resign others prefer to increase their effort. We show that different effort costs and beliefs about the own ability and the production function together with Bayesian updating can explain differences in behavior; different ex-ante beliefs about the sources of success are not needed.

ABSTRACT. Decision makers with time-inconsistent preferences have been studied in great detail in recent decades. Addressing the dearth of literature on time inconsistency in a strategic context, our work provides the foundations for dealing with two-player games with naive and sophisticated players. We model various types' beliefs explicitly, and then proceed to define equilibrium notions based on these belief hierarchies. Second-order beliefs of naive players turn out to be crucial, and lead to different equilibria even in relatively simple games. We provide several examples, including models of bargaining and bank runs, showing the applicability of our framework.

ABSTRACT. This paper studies two-player games in continuous time with imperfect public monitoring, where information may arrive both continuously, governed by a Brownian motion, and discontinuously, according to Poisson processes. For this general class of two-player games, we characterize the equilibrium payoff set via a differential equation of its boundary. The equilibrium payoff set is obtained from an iterative procedure similar to that known in discrete time. In our setting, however, the resulting payoff set in each step of the iteration is characterized explicitly. Our analysis reveals the drastic influence of abrupt information on the equilibrium payoff set: because of the additional possibility for value burning, the equilibrium payoff set extends much closer to the efficient frontier and its boundary may contain additional straight line segments.

ABSTRACT. McLennan and Tourky (2010) showed that "imitation games" provide a new view of the computation of Nash equilibria of bimatrix games with the Lemke-Howson algorithm. In an imitation game, the payoff matrix of one of the players is the identity matrix. We study the more general "unit vector games", which are already known, where the payoff matrix of one player is composed of unit vectors. Our main application is a simplification of the construction by Savani and von Stengel (2006) of bimatrix games where two basic equilibrium-finding algorithms take exponentially many steps: the Lemke-Howson algorithm, and support enumeration.

ABSTRACT. In a symmetric two-player game, a symmetric equilibrium can only be dynamically stable if it has positive index. The sum of the indices of all equilibria is 1, so a unique equilibrium has index 1. The index is a topological notion related to geometric orientation, and defined in terms of the sign of the determinant of the payoffs in the equilibrium support. We prove a simple strategic characterization of the index conjectured by Hofbauer: In a nondegenerate symmetric game, an equilibrium has index 1 if and only if it is the unique equilibrium in a larger symmetric game obtained by adding further strategies (it suffices to add a linear number of strategies). Our proof introduces unit-vector games where one player's payoff matrix consists of unit vectors, and applies in a novel way simplicial polytopes and a known result that any matrix with positive determinant is the product of three P-matrices.

ABSTRACT. The fixed point index assigns an index of +1 or -1 to each fixed point of a generic function or correspondence, and these indices sum to +1. If an isolated equilibrium is stable with respect to any process of adjustment to equilibrium that is economically ``natural,'' then the index of the equilibrium is +1. The index +1 principle asserts that consequently only index +1 equilibria are empirically relevant; we argue that this should be regarded as a fundamental principle of economic analysis. The index +1 principle is universally applicable to economic models in which equilibria are topological fixed points. It does not depend on insignificant details of model specification. The index +1 principle itself, and the hypothesis that processes of adjustment to equilibrium are natural, are strongly supported by experimental evidence. The index +1 principle can be seen as the multidimensional extension of Samuelson's correspondence principle.

ABSTRACT. A dynamic game of experimentation is examined where players search for an unknown threshold. Players contribute to the rate of decline in a state variable, and the game ends with a costly breakdown once the state falls below the threshold. In the unique symmetric pure-strategy stationary Markov equilibrium, the state decreases gradually over time and settles at a cutoff level asymptotically, conditional on no breakdown. The cutoff depends on the patience, the cost of the breakdown, and the prior distribution of the threshold, but not on the number of players. In a discrete-time version of the game, the equilibrium time path of the state converges to that of the continuous-time model when period length tends to zero.

ABSTRACT. In this paper, I examine the effect of introducing heterogeneity between players in a model of strategic experimentation. I consider a two-armed bandit problem in continuous time with one safe and another risky arm. I show that if the degree of heterogeneity between the players is high enough, then there exists a unique Markov perfect equilibrium in simple cutoff strategies. For moderate level of heterogeneity cutoff equilibrium exists along with other equilibria, but the cut-off equilibrium Pareto dominates other equilibria. For low level of heterogeneity, no cutoff equilibrium exists and at some instances, the most heterogeneous equilibrium Pareto dominates all other equilibria.

ABSTRACT. I study a game of strategic experimentation with two-armed bandits in which the state of the world is restless, "reboots" at exponentially distributed random times. Players observe neither the initial state of the world nor reboot times, but may learn about whether the current state is good via news that arrives at exponential times. Unlike in standard good-news models of strategic experimentation in which the state is rested, there are parameters for which the encouragement effect is present and players experiment beyond the single-player threshold. There also exists a range of parameters for which the free-riding effect is mute and the equilibrium is efficient.

ABSTRACT. In this paper, a contest designer derives profits from aggregate effort exerted by the contestants. I develop a revelation mechanism that enables the contest designer to select a subset of contestants from a pool of candidates in a way that maximizes her profits, even though she is uninformed about the candidates' valuations for the contest prize. I prove the existence of an incentive compatible mechanism. I solve the designer's problem by using a 3-stage game where at Stage 0, the designer designs a mechanism, at Stage 1 the contestants participate in the mechanism then contestants are selected and at Stage 2, information is revealed and the selected contestants participate to a contest. Depending on the marginal cost that a contestant imposes on the designer, some candidates with a low valuation for the contested good may never be selected to the contest.

ABSTRACT. This paper considers dynamic resource allocation processes, called iterative revelation mechanisms, with quasi-linear dichotomous utilities and complete information. Agents gradually reveal their valuation through ``ask-price'' binary questions. The social planner identifies the efficient outcome, and monetary transfer is determined on a ``pay-as-bid'' basis. We show that the efficient allocation rule is implemented in a subgame perfect Nash equilibrium, regardless of details of an ask-price process. The analysis applies to the case with limited communication, and every strongly monotone allocation rule is implemented in equilibrium. We also show that if a resource allocation process is ex post incentive compatible, it is an ascending-price mechanism. In a single-object allocation problem, the English auction is a unique mechanism satisfying efficiency, ex post incentive compatibility, and pay-as-bid transfer.

ABSTRACT. A group of individuals is choosing an individual (the winner) among themselves, when the identity of the deserving winner is a common knowledge among individuals. A simple mechanism of voting by veto is proposed as an alternative to the mechanism studied by Amorós (2011). Like Amorós'(2011), the suggested mechanism implements the socially desirable outcome (the deserving winner is chosen) in subgame perfect equilibria.

ABSTRACT. An agent chooses among projects with random outcomes. His payoff is increasing in the outcome and in the observer's expectation of the outcome. With some probability the agent can disclose the true outcome to the observer. We show that choice is inefficient: the agent favors riskier projects even with lower expected returns. If information can also be disclosed by a challenger who prefers lower beliefs of the observer, the chosen project is excessively risky when the agent has better access to information than the challenger, excessively risk-averse when the challenger has better access, and efficient otherwise. We also characterize the agent's worst-case equilibrium payoff.

ABSTRACT. This study investigate experimentally the revelation of verifiable information in a market setting. We find that sellers often choose to report a selected set of information and buyers on average compensate for this by bidding less. A higher level of competition has a positive and significant effect on the revelation of information on the seller side. In both the monopoly and the competition setting, the buyers are on average not able to fully compensate the sellers' selection of evidence. The bids significantly exceed the values of the good in both treatments, leading to a payoff difference in favor of the sellers. 25% of the buyers' bids do not account for the selection in evidences.

ABSTRACT. We analyze a model of competition in Bayesian persuasion in which two or more senders vie for the patronage of a receiver by disclosing information about their respective proposals. We focus particularly on binary state space, i.e., each sender’s proposal gives the receiver either a high or low utility. With two (possibly asymmetric) senders, we fully characterize the generically unique equilibrium and show that its simple linear structure similar to that of all-pay auction with complete information. A sender facing a stronger opponent engages in more aggressive disclosure in terms of second-order stochastic dominance. With multiple symmetric senders, an increase in the number of competing senders leads to a more aggressive disclosure, which converges to full disclosure as the number of senders goes to infinity. Finally, we show that the finding that equilibrium strategy must exhibit a linear structure remains valid locally for any finite state space model.

ABSTRACT. I study an observational learning model over general social networks where Bayesian agents endogenously acquire information through costly search. Agents arrive in sequence and take a single decision each. The qualities of the two feasible actions are a priori unknown to the agents. Each individual observes the actions of a stochastically generated neighborhood of individuals (network topology). Then, the agent engages in private sequential search to finally select an action among those he has sampled. Asymptotic learning occurs if search costs are not bounded away from zero, the network topology is sufficiently connected and: either neighborhood realizations convey little information about the network; or information asymmetries are described through beliefs over the states of a finite Markov chain. When the network topology is not sufficiently connected, asymptotic learning always fails. For search costs that are bounded away from zero, I introduce and study the weaker notion of maximal learning.

ABSTRACT. We introduce a model for coalitional network stability in networks with widespread externalities. The network function form generalises the partition function form of cooperative games in allowing the network structure to be taken into account. The recursive core for network function form games generalises the recursive core for such environments and its properties also rhyme with the corresponding inclusion properties of the optimistic and pessimistic recursive cores and can be seen as a modification of pairwise stability to a coalitional setting where the involvement of more players allows for the -- partial -- internalisation of the externalities, but we also allow residual players to endogenously respond to any externalities that may affect them. We present a simple example of a favour network and show that the core is nonempty when players must pay transfers to intermediaries. This simple setting also models economic situations such as airline networks.

ABSTRACT. The concept of community in complex networks, which is intuitively expressed as a group of nodes more densely connected to each other than to the rest of the network, has not been formally defined yet in a manner that encompasses all aspect ensuing from this intuitive description. Among existing approaches, a popular one consists in considering the network community structure as optimum value of a fitness function that reflects the modularity of the network. Recently, a new trend to model the problem as a game having the community structure as equilibrium has emerged. Both approaches are appealing as they allow the design of heuristic approaches to this problem and benefit from their adaptability and scalability. This paper analyzes the behavior of such a heuristic that is based on extremal optimization in combination with two possible game theoretic models that consider different payoff functions, in comparison with the corresponding optimization approaches.

ABSTRACT. This paper uses a game of mini poker to highlight the importance of the typical assumption that players know each other's risk attitude. We solve the game under both perfect and incomplete information about risk types. With perfect information we fully characterise a unique equilibrium for all possible risk types and show that both bluffs and uncertain calls occur with positive probability for some types. In the second case player's beliefs about risk types are given by an arbitrary probability distribution over the set of all possible risk types. We prove existence and uniqueness, and fully characterise equilibrium. We find: a) the set of bluffing types and the set of types who make uncertain calls are non-degenerate and b) these sets are never identical and never disjoint but, for certain beliefs, the set of bluffing types is a proper subset of the set of types who make uncertain calls.

ABSTRACT. We extend previous work on complete information all-pay auctions to incorporate heterogeneous risk and loss averse utility functions. We provide sufficient and necessary conditions for the existence of equilibria with a given set of active players and characterize those equilibria. Focusing on the equilibria in which all active players randomize continuously between zero and the (common) value of the prize, we found, surprisingly, that when players are heterogeneous in their risk(/loss) aversions, the more risk averse players either dropout or bid higher than the less risk averse players. Moreover, players' expected bids decrease with others' risk aversions, but increase with own risk aversions. If the risk aversion of a less risk averse player is increased, then total expected bid increases. When there are only two types of risk aversions, we show the sufficient condition for total expected bid to increase with the share of the more risk averse players.

ABSTRACT. We examine bidding behavior in first-price sealed-bid and Dutch auctions, which are strategically equivalent under standard preferences. We investigate whether the empirical breakdown of this equivalence is due to (non-standard) preferences or due to the different complexity of the two formats, i.e., a different level of mathematical or individual sophistication. First, we elicit measures of individual preferences and secondly manipulate the degree of complexity by offering various levels of decision support. Our results show that the equivalence of the two auction formats only breaks down in the absence of decision support. This indicates that the empirical breakdown is caused by differing complexity between the two formats rather than non-standard preferences.

ABSTRACT. In strategic-form games, that is, Selten's (1975) perfect equilibria are admissible. This is not true for extensive-form perfection. Quasi-perfect equilibria uses Selten's (1975) trembles to introduce a refinement of Nash equilibrium wherein each player puts infinitessimal weight on \emph{other players's} strategies, but not her own. One might be sure of oneself while (infinitessimally) unsure of others. However, also quasi-perfection is not itself without problems, precisely because it ignores future infinitessimal uncetainties in one's own play. We introduce a refinement here perfect quasi-perfect equilibrium, that tries to take keep the advantages of both, perfect and quasi-perfect equilibrium, while at the same time avoids the disatvantages of these two concepts. Our idea is to force each player to consider infinitessimal deviations in his own future play, but to make them so unlikely that they are infinitely less likely than the combined likelihood of deviations by all other players.

ABSTRACT. Extensive-form games constitute the standard representation scheme for games with a temporal component. But do all extensive-form games correspond to protocols that we can implement in the real world? We often rule out games with imperfect recall, which prescribe that an agent forget something that she knew before. In this paper, we show that even some games with perfect recall can be problematic to implement. Specifically, we show that if the agents have a sense of time passing (say, access to a clock), then some extensive-form games cannot be implemented; no matter how we time the game, some information will leak to the agents that they are not supposed to have. We say such a game is not exactly timeable and provide easy-to-check characterization of exactly timeable games. We hope to convince the reader that timeability should be a standard assumption, just as perfect recall is today.

ABSTRACT. We consider how to extend Kreps and Wilson.s 1982 definition of sequential equilibrium to multi-stage games with infinite sets of types and actions. A concept of open sequential equilibrium is defined by taking limits of strategy profiles that can consistently satisfy approximate sequential rationality for all players at arbitrarily large finite collections of observable open events. Existence of open sequential equilibria is shown for a broad class of regular projective games. Examples are considered to illustrate the properties of this solution and the difficulties of alternative approaches to the problem of extending sequential equilibrium to infinite games.

ABSTRACT. This talk has been cancelled.

ABSTRACT. In many applications of coalition formation games, a key issue is that some desirable coalition structures are not elements of the core of these games. In these cases, it would be useful for an authority which aims to implement a certain outcome to know how far from the original game is the nearest game where the desirable outcome is part of the core. This question is at the center of this study. Focusing on hedonic games, we uncover previously unexplored links between such games and transferrable utility games and develop a tailor-made solution concept for the transferrable utility game, the implementation core, to provide an answer to our question.

ABSTRACT. In this paper a new class of relaxed sequencing games is introduced: the class of Step out - Step in sequencing games. In this relaxation any player within a coalition is allowed to step out from his position in the processing order and to step in at any position later in the processing order. First, we show that if the value of a coalition in a relaxed sequencing game is bounded from above by the gains made by all possible neighbor switches, then the game has a non-empty core. After that, we show that this is the case for Step out - Step in sequencing games. Moreover, this paper provides a polynomial time algorithm to determine the values of the coalitions in Step out - Step in sequencing games.

ABSTRACT. We consider an infinite-horizon model of elections where changes in policies are costly for citizens and parties. The so-called costs of change increase with the extent of the policy shift. If the initial level of policy polarization is low, we find that welfare is maximal--and policy polarization is minimal--for intermediate marginal costs of change. Moreover, non-zero costs of change are never welfare-reducing, provided that the future is sufficiently valuable to society. If the initial level of policy polarization is high, however, welfare is only maximal for low or zero costs of change. We also show that, in our framework, there exists a welfare-increasing re-election hurdle above 50% if and only if the initial level of policy polarization is intermediate and the social discount factor is sufficiently large.

ABSTRACT. We consider the class of voting by committees to be used by a society to collectively choose a subset of a given set of objects. We offer a simple criterion to compare two voting by committees without dummy agents according to their manipulability. This criterion is based on the set-inclusion relationships of the two corresponding decisive and vetoer sets of agents. We show that the binary relation "to be as manipulable as" endows the set of equivalence classes of anonymous voting by committees (i.e., voting by quotas) with a complete upper semilattice structure, whose supremum is the equivalence class containing all voting by quotas with the property that the quota of each object is strictly larger than one and strictly lower than the number of agents. Finally, we extend the comparability criterion to the full class of all voting by committees.

ABSTRACT. Social psychology, as opposed to economics, argues that individual behavior is socially determined. For instance, self-categorization theory (SCT) argues that an individual's cognition of self occurs through a process of drawing similarities with certain social categories (the ingroup) and distinctions from others (the outgroup). Further, individual behavior embodies a sense of depersonalization, reflecting group attitudes rather than inherent tastes. In this paper, we study whether the traditional notion of rational behavior in economics can be reconciled with this worldview. Specifically, we ask whether an individual who is born into a society of rational inhabitants, can learn to behave rationally based on observing these inhabitants' choices and internalizing this data through the prism of a process akin to self-categorization? We introduce a condition on this individual's ingroup-outgroup categorization that draws on the concept of a category prototype in SCT which allows us to answer this question in the affirmative.

ABSTRACT. We study whether coordination failure is more often overcome if players can easily disclose their actions. In an experiment subjects first choose their action and then choose whether to disclose this action to other group members, and disclosure costs are varied between treatments. We find that no group overcomes coordination failure when action disclosure costs are high, but half of the groups do so when the costs are low. Simulations with a belief learning model can predict which groups will overcome coordination failure, but only if it is assumed that players are either farsighted, risk-seeking or pro-social. To distinguish between these explanations we collected additional data on individual preferences and the degree of farsightedness. We find that in the low cost treatment players classified as more farsighted more often deviate from an inefficient convention and disclose this action, while the effect of risk and social preferences is not significant.

ABSTRACT. Why do diverse groups outperform homogeneous groups in some settings, but not in others? We show that while diverse groups experience more frictions than homogeneous ones, they are also less conformist. Homogeneous groups minimize the risk of miscoordination, but they may get stuck in an inefficient equilibrium. Diverse groups may fail to coordinate, but if they do, they tend to attain efficiency. This fundamental tradeoff determines how the optimal level of diversity varies with social and economic factors. When it is vitally important to avoid miscoordination, homogeneous groups are optimal. However, when it is critical to implement new and efficient practices, diverse groups perform better.

ABSTRACT. I discuss a new way to understand agents' preferences - "demand types" - developed in my work with Elizabeth Baldwin. Our methods give new results about when competitive equilibrium exists with indivisibilities. They also help develop extensions to the Product-Mix Auction I invented for the Bank of England in response to the financial crisis. Other applications include coalition-formation and matching models.

ABSTRACT. We investigate how information (e.g., digital goods, innovation, news) is priced and diffused across the links of a network. Every player who acquires information enjoys an idiosyncratic consumption value and may subsequently replicate and resell it to uninformed neighbors. A partition of the network describes how profit division among players depends on the positions of the initial sources of information. Two nodes belong to the same block of the partition if they are connected by a unique path in an auxiliary network. Information enters each block not containing a seller through the same node - the dealer of the block. Dealers can acquire information from multiple neighbors and obtain it for free due to competition among sellers. Each seller has monopoly power over the buyers in his block and extracts a share of their values. Links within blocks constitute bottlenecks and are essential for connecting the network and diffusing information. Links bridging distinct blocks are redundant for connectivity and impose negative externalities on sellers.

ABSTRACT. Akerlof (1970) argues that the superior information often held by sellers leads to market failure, since high quality sellers are unwilling to sell at the prevailing market price. If sellers can certify their quality, information unravels because high quality sellers have the biggest incentive to certify in order to receive a high price. We consider a privately informed seller who can propose any selling mechanism to a buyer. Values are interdependent, so the seller's reservation value or cost and the buyer's valuation can depend both on the buyer's taste and on product characteristics. Product information is voluntarily and costlessly certifiable by the seller. While the seller's certification ability enlarges the set of feasible selling procedures because it relaxes his incentive constraints, it also makes deviations more compelling as a high-type seller can deviate and provide evidence of his quality. We characterise all feasible allocations under any certifiability structure, formulate the informed-principal mechanism-proposal game and describe a canonical certification and communication protocol. We show that there is always an ex-ante profit-maximizing selling procedure that is an equilibrium of the (interim) mechanism-proposal game. In general, posted prices are sub-optimal and in contrast to the case where the seller can only post prices, his ability to certify increases profits compared to the case where his product information is public, both from the ex-ante and the interim perspectives. The unravelling outcome may not be an equilibrium even when all buyer types agree on the ranking of product quality. Under further assumptions analogous to ones in Maskin and Tirole (1990), we show that all equilibrium outcomes are ex-ante profit-maximising.

Joint work with Frederic Koessler.

ABSTRACT. Posted price mechanisms are simple, straightforward, and strategyproof. We study two scenarios of combinatorial markets where sequential posted price mechanisms achieve optimal or nearly optimal welfare. The first scenario is matching markets with full information, where optimal welfare is obtained. The second is markets with submodular (and XOS) valuations with Bayesian information, where half of the optimal welfare is obtained. We distinguish between static and dynamic pricing, and present various extensions of the above findings. Finally, we mention surprising relations between price of anarchy results and posted price mechanisms.

Based on joint works with Vincent Cohen-Addad, Alon Eden and Amos Fiat (2016), with Nick Gravin and Brendan Lucier (2015) and with Paul Duetting, Thomas Kesselheim and Brendan Lucier (2016).

ABSTRACT. Following Dietrich (2014) we consider using choice by plurality voting (CPV) as a judgment aggregation correspondence. We notice that a result of Roberts (1991) implies that CPV is axiomatically characterized by anonymity, neutrality, unanimity, and (Young's) reinforcement. Following List (2004) and Dietrich (2015) we construct a sequential voting procedure of judgement aggregation which satisfies rationality, anonymity, unanimity, and independence of irrelevant propositions (with respect to a relevance correspondence that does not satisfy transitivity). We intend to characterize this aggregation procedure by a set of axioms.

Joint work with Bezalel Peleg.

ABSTRACT. User-friendly websites applying theoretical methods to share private items require simple preference domains, such as linear preferences. I will survey recent research focusing on the familiar "equal opportunities" approach to fair division: there are good news and bad news.

If the items are divisible goods the Competitive Equilibrium with Equal Incomes maximizes the Nash product of utilities and is normatively superior to its nemesis equalizing relative gains. It is characterized by the following invariance property: changing my bid on a good I am not consuming before or after the change, does not affect the allocation at all.

If the items are indivisible, maximizing the Nash product still delivers an approximately envy-free division, thus respecting the spirit of the Competitive approach.

If the items are divisible bads, the Competitive solution still identifies critical points of the Nash product of utilities, but there may be many such welfare-distinct outcomes (in the order of 2^n with n agents and n bads). The set of envy-free and efficient allocations can similarly have many connected components, implying that no efficient and envy-free division method can vary continuously in the parameters of the problem.

A similarly unsettling picture comes up in the assignment problem where the total share of each participant is fixed: the Competitive solution is guaranteed to exist but may again deliver multiple divisions among which it appears difficult to provide a plausible selection argument.

These results uncover some limits of single-valued deterministic fair division rules.

ABSTRACT. We study multidimensional mechanism design in a common scenario where players have private information ab out their willingness to pay and their ability to pay. We provide necessary and sufficient conditions for the dominant-strategy incentive-compatible implementability of direct mechanisms for the general case where players can arbitrarily misreport their private budgets. Immediate practical applications of these results include simple complete characterizations for mechanisms with publicly-known budgets and for mechanisms where over-reporting the budget is not possible. The celebrated revenue equivalence theorem states that the seller’s revenue for a broad class of standard auction formats and settings will b e the same in equilibrium. Our main application is a revenue equivalence theorem for financially-constrained multidimensional bidders

ABSTRACT. We analyze mechanism choices of competing sellers with private valuations and show the existence of monotone pure strategy equilibria where sellers with higher reservation value choose mechanisms with a lower selling probability and a larger revenue in case of trade. As an application we investigate the choice between posted prices and auctions and demonstrate that sellers refuse to offer posted prices as long as (risk-neutral) buyers do not differ with respect to their transaction costs in both trade institutions. If some buyers have lower transaction costs when trading at a posted price, it is optimal for sellers to offer posted prices if and only if they have sufficiently high reservation value. We develop an empirical strategy to compare revenues of posted prices and auctions that takes selling probabilities explicitly into account, and confirm our theoretical predictions with data from eBay auctions on ticket sales for the EURO 2008 Football Championship.

ABSTRACT. In a mechanism design setting with quasilinear preferences, a domain D of admissible valuations of an agent is called a monotonicity domain if every 2-cycle monotone allocation rule is truthfully implementable (in dominant strategies). D is called a revenue equivalence domain if every implementable allocation rule satisfies revenue equivalence. Carbajal and Muller (2015) introduced the notions of monotonic transformations in differences and showed that if D admits these transformations then it is a revenue equivalence and monotonicity domain. Here we show that various economic domains, with countable or uncountable allocation sets, admit monotonic transformations in differences. Our applications include public and private supply of divisible public goods, multi-unit auction-like environments with increasing valuations, allocation problems with single-peaked valuations, and allocation problems with externalities.

ABSTRACT. We study, both theoretically and experimentally, the impact of public and secret reserve prices in second price auctions where buyers have independent private values and heterogeneous entry costs. In such settings it is known that public reserve prices are more optimal than secret reserve prices. Paradoxically, secret reserve prices are commonly used in practice. We show that when the auctioneer is risk averse, optimal secret and public prices move closer together. In our experiment, we observe little difference in secret and publicly chosen reserves, and revenue is greater in the secret reserve. We propose several explanations in terms of bidder and auctioneer using boundedly rational behaviour.

ABSTRACT. We construct the generalized Créemer-McLean mechanism where i's participation fee depends not only on the valuations reported by -i at the second stage, but also on the choice of the participation fee by -i at the first stage. Such construction allows to exploit the convex hull property of beliefs whenever it appears in beliefs about beliefs rather than in beliefs about preferences. As such betting mechanism retrieves agents' entire hierarchies of beliefs, it reveals what is common knowledge among them. Hence, for any given countable collection of type spaces {T}^k, k in K, each T^k verifying the convex hull property within itself, the designer can propose a union of GCM mechanisms and extract the surplus across type spaces, i.e. regardless of absence of knowledge by the designer of agents' type space. We discuss when the technique of using a union of individual mechanisms is extendible to more general cases.

ABSTRACT. Bidding in first-price auctions crucially depends on the beliefs of the bidders. We analyze bidding behavior in a first-price auction in which the knowledge of the bidders about the distribution of the values of their competitors is restricted to the range and the mean. To model this situation, we assume that under such uncertainty a bidder will expect to face the distribution of values that minimizes her expected payoff, given her bid is an optimal reaction to the bids of her competitors induced by this distribution. This introduces a novel way to endogenize beliefs in games of incomplete information. We find that that even though the worst case beliefs are type dependent in a non-monotonic way, an efficient equilibrium of the first-price auction exists.

ABSTRACT. Best-reply behavior in Cournot oligopolies generally leads to Cournot-Nash equilibrium, but imitative behavior selects the Walrasian equilibrium as the unique stochastically stable state. Previous work (Alós-Ferrer, 2004) showed that in the presence of non-trivial memory, imitative behavior leads to a non-trivial dynamics selecting all quantities between the Cournot and Walrasian outcomes. However, the scope of previous results was limited to specific assumptions on demand and cost functions, and did not provide information on the shape of the distribution of outcomes. We use computational simulations to address these limitations. We show that the selection result for non-trivial memory holds beyond the set of well-behaved Cournot games previously analyzed. Further, we shed light on the exact shape of the limit distribution in Cournot games. We find that it is highly skewed towards the Walrasian quantity. Although longer memory increases the importance of the Cournot equilibrium, the competitive outcome remains the dominant prediction.

ABSTRACT. This paper proves an equilibrium selection result for a class of games with strategic substitutes. Specifically, for a general class of binary action, N-player games, we prove that each such game has a unique equilibrium strategy profile. Using a global game approach first introduced by Carlsson and van Damme (1993), important selection results apply to games with strategic complementarities. The present paper uses the same approach but removes the assumption of perfect symmetry in the "dominance region" of the players' payoffs. Instead we assume that players are ordered such that asymmetric dominance regions are overlapped sequentially. This allows us to extend selection results to a class of games with strategic substitutes.

ABSTRACT. We study a single product market with affine inverse demand function in which two producers/retailers, producing under capacity constraints, may order additional quantities from a single profit maximizing supplier. We express this chain as a two stage game and show that it has a unique subgame-perfect Nash equilibrium. If the supplier faces uncertainty about the demand intercept and whenever a Bayesian Nash equilibrium exists, the supplier's profit margin at equilibrium is a fixed point of a translation of the MRL function of his belief under the assumption that his belief is non-atomic and the retailers are identical. If the supplier's belief is of Decreasing Mean Residual Lifetime (DMRL), the game has a unique subgame-perfect Bayesian Nash equilibrium. Inefficiencies at equilibrium generated by the lack of information of the supplier are investigated, and examples are provided. Finally, the main results are generalized for more than two identical producers/retailers.

ABSTRACT. This study sets a bank-run equilibrium analysis in a dynamic and incomplete information environment where agents can reconsider attempts to run on the bank over time. The typical static bank-run model is extended in this paper to capture the learning dynamics of agents through time, giving bank-run analysis a more realistic feature. Apart from employing a self-fulfilling framework in this model, we allow agents to update over time their beliefs on the strength of the fundamentals that is not commonly known. In particular, we extend the bank-run model analyzed by Goldstein and Pauzner (2005) and build it on a dynamic global games framework studied by Angeletos et.al. (2007). We present here how a simple recursive setup can generate a unique monotone perfect Bayesian equilibrium and show how the probability of bank-run is affected over time by the inflow of information and the knowledge of previous state outcome.

ABSTRACT. We answer the following question: Does regulating the banking network increase systemic risk in the entire financial network in the presence of unregulated shadow banks? To answer this question we construct a discounted stochastic game model of network formation. The stationary Markov network formation strategies of the players, then give rise to the equilibrium network formation dynamics.We then provide a formal definition of systemic risk based on the induced equilibrium dynamics, and therefore, a definition which takes into account the strategic interactions of financial institutions when facing different regulatory policies. Specializing our dynamic stochastic game model to a more basic model in which banks and shadow banks form a network including connections to the real economy, we show, via numerical simulations under various regulatory regimes, that imposing bank regulations not faced by shadow banks does indeed increase systemic risk throughout the financial network.

ABSTRACT. In this work we introduce a Perfect Equilibrium notion, in vein of Selten(1975), for the unanimity multiplayer bargaining. The need for this concept is justified by the existence of some SPNE strategies where players use some dominated actions, vide Haller (1986). The new concept poses some conceptual and technical difficulties that we herein address.

ABSTRACT. Many negotiations (for instance, among political parties or partners in a business) are characterized by dynamic bargaining: current agreements affect future bargaining possibilities. We study such situations using bargaining games á la Rubinstein (1982), with the novelty that players can decide how much to invest, as well as how to share the residual surplus for their own consumption. We show that under certain conditions, there is a unique (stationary) Markov Perfect Equilibrium characterized by immediate agreement. Moreover, standard results in bargaining theory can be overturned. For instance, despite the complexity of the bargaining game, there are equilibrium strategies as in an ultimatum, where the responder does not consume anything. Also, a more patient proposer may consumes less than his opponent. Additionally, a higher discount factor for one player may decrease the MPE investment rates for both players.

ABSTRACT. We consider bargaining problems that are star-shaped. Convex and comprehensive bargaining problems are star-shaped but not conversely. We present a class of economic environments generating star-shaped bargaining problems. We completely characterize single-valued solutions satisfying the Nash axioms on the class of star-shaped and compact bargaining problems. For the case with two players, we show that there are exactly two solutions with each being a selection of Nash product maximizers in favor of a given player across all bargaining problems. We design a non-cooperative extensive-form game to implement these solutions, and we extend our analysis to allow for asymmetries and for more than two players.

ABSTRACT. This paper introduces a dynamic matching mechanism in which a persistent contracting relationship - an "old boys' club" - occurs in ex post subgame perfect Nash equilibrium when the high school in the club is sufficiently patient. Matching occurs in two stages: first, contracting between the college and a high school; second, running a Vickrey auction in the simplified post-contracting admissions market. The mechanism provides the second best total surplus among several mechanisms in a repeated college admissions market in which externalities preclude solutions using standard mechanism and market design techniques. An "old boys' club" emerges between one college and a sufficiently patient single high school as a consequence of contract enforcement rather than ex ante bias on the part of the college. Members of the club benefit at the expense of the non-contracted high school.

ABSTRACT. In many real-life two-sided markets, one side of the markets is partitioned into groups. Groups run their own admission process independently of one another. For such markets Manjunath and Turhan introduce iterative deferred acceptance algorithm that yields a stable matching (possibly different from extremal ones depending on partitions). In this paper, we study the effect of partition structures on agents' welfare and incentives under this stable mechanism in the context of marriage model. The algorithm finds the men-optimal stable matching under the coarsest partition of the set of women and the women-optimal stable matching under the finest partition of the set of women. We find that when women partition gets finer, men get weakly worse off. Also, if women partition gets finer, the iterative deferred acceptance rule becomes more manipulable for men. Our results have significant policy implications especially in school choice problems when stability is the primary policy goal.

ABSTRACT. We examine assignment games, where matched pairs of firms and workers create some monetary value to distribute among themselves. In the majority of this literature, externalities - in the sense that a pair’s value depends on the pairing of the others - have been neglected. However, in most applications a firm’s success depends on the success of its rivals. Thus, it is natural to ask how the classical results on assignment games are affected by the introduction of externalities? The answer is – dramatically. We find that a problem may have no stable outcome, stable outcomes can be inefficient, efficient outcomes can be unstable, and the set of stable outcomes may not form a lattice. We show that stable outcomes always exist if agents are "pessimistic". This is a knife-edge result: there are problems in which the slightest optimism by a single pair erases all stable outcomes.

ABSTRACT. We consider the problem of allocating sets of objects to agents and collecting payments. Each agent has a preference relation over the set of pairs consisting of a set of objects and a payment. Preferences are not necessarily quasi-linear. Non-quasi-linear preferences describe environments where the wealth effect is non-negligible: the payment level changes agents' willingness to pay for swapping sets. Preferences satisfy the object monotonicity, that is, when the payment level is fixed, agents always prefer to receive more objects. We investigate when it is possible to design strategy-proof and efficient rules, that is, on which domains such rules exist, and show that (i) for two agents, each "r-partially-quasi-linear" domain is a maximal domain for efficiency and strategy-proofness, and (ii) for more than two agents, if a domain includes a class of r-partially quasi-linear preferences, no rule is efficient and strategy-proof.

ABSTRACT. Agents frequently have different opinions on where to locate a public facility. While some agents consider the facility a good and prefer to have it nearby, others dislike it and would like to see it built far away from their own locations. To aggregate agents' preferences in these situations, we propose a new preference domain according to which each agent is allowed to have single-peaked or single-dipped preferences on the location of the facility, but in such a way that the peak or dip is situated in her own location. We characterize all strategy-proof rules in this general framework and show that they are also group strategy-proof. Finally, we characterize for some focal cases the rules that additionally satisfy Pareto efficiency.

ABSTRACT. We consider collective decision problems where some agents have private information about alternatives and others don't. Voting takes place under strategy proof rules. Prior to voting, informed agents may or may not disclose their private information, thus eventually influencing the preferences of those initially uninformed. We provide general conditions on the voting rules guaranteeing that informed agents will always be induced to disclose what they know. In particular, we apply this general result to environments where agent's preferences are restricted to be single-peaked or separable, and characterize the strategy proof rules that ensure information disclosure in these settings.

ABSTRACT. This paper studies repeated games in which players evaluate payoff streams by recursive utility. Focusing on pure strategies, we investigate feasible payoffs and subgame perfect equilibrium payoffs of a repeated game. Previous studies have shown that, with recursive utility, non-stationary paths can yield repeated-game payoffs that cannot be generated by convex combinations of constant paths. We first characterize the set of feasible payoffs in the repeated game using the idea of self-generation. Then, we present a folk theorem that provides conditions on recursive utility under which any sequentially individually rational path can be supported in a subgame perfect equilibrium when players are sufficiently patient. Lastly, we discuss the role of alternating paths, providing examples to illustrate that players' attitude toward time variability can affect their behavior in repeated games.

ABSTRACT. Does the modeler neglect some equilibria if he ignores unlikely and temporary changes of the payoff matrix in repeated relationships? This question is addressed in this paper by offering a robustness test for predictions in finitely repeated games. It is shown that the set of feasible and rational payoffs is the unique robust equilibrium payoff set, when the horizon is large and the discount factor tends to 1. Consequently, cooperation can arise as an equilibrium behavior in a game arbitrarily close to the standard prisoner’s dilemma, if the horizon is finite but sufficiently long and if players are sufficiently patient.

ABSTRACT. We consider two-player repeated where the players observe their own payoffs. We prove that any strictly efficient payoff can be obtained as sequential equilibrium payoff, when costly communication is available and the players are sufficiently patient.

ABSTRACT. We study decentralized learning dynamics for the assignment game. At random points in time firms and workers match, break up, and re-match in the search for better opportunities. We propose a simple learning process in which players have no knowledge about other players' payoffs or actions and they update their behavior in a myopic fashion. Behavior fluctuates according to a random variable that reflects current market sentiment: sometimes the firms exhibit greater price stickiness than the workers, and at other times the reverse holds. We show that this stochastic learning process converges in polynomial time to the core. While convergence to the core is known for decentralized dynamics this paper is the first to prove polynomial time convergence, a crucial feature from a practical standpoint. The proof relies on novel results for random walks on graphs, and suggests a fruitful connection between the theory of random walks and matching theory.

ABSTRACT. In this paper, we investigate gains from strategy revisions in deterministic evolutionary dynamics in continuous population. To clarify the gain from revision, we construct an evolutionary dynamic from optimal decision with stochastic (possibly restricted) available action set and switching cost. Many of major non-imitative dynamics can be constructed in this framework. We formally define expected gains and obtain several general properties of the expected gain function, which leads to Nash stability in contractive games---generalization of concave potential games. The unified framework allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is observable or unobservable. This extends the known positive result on evolutionary implementation of social optimum through Pigouvian pricing to the presence of heterogeneity and non-aggregate payoff perturbations.

ABSTRACT. Given a two-player zero-sum discounted-payoff stochastic game, we introduce three classes of continuous-time best-response dynamics: open-loop best-response dynamics, stopping-time best-response dynamics, and closed-loop best-response dynamics. We show the global convergence of the latter two classes to the set of optimal strategy profiles, which can thus be viewed as a dynamical proof of the existence of value in these games. We show the convergence of the first class when the players are sufficiently impatient. We also show that the payoffs in a modified closed-loop best-response dynamic converge to the asymptotic value in a zero-sum stochastic game.

ABSTRACT. Two heterogeneous agents exert effort over time to complete a project and collectively decide its scope. A larger scope requires greater cumulative effort and delivers higher benefits upon completion. To study the scope under collective choice, we derive the agents’ preferences over scopes. The efficient agent prefers a smaller scope, and preferences are time-inconsistent: as the project progresses, the efficient agent’s preferred scope shrinks, whereas the inefficient agent’s preferred scope expands. In equilibrium without commitment, the efficient agent obtains his ideal project scope with either agent as dictator and under unanimity. In this sense, the efficient agent always has real authority.

ABSTRACT. Many mechanisms have been developed to solve the free-rider problem in private public good provision. I present a new class of mechanisms, the Conditional Contribution Mechanisms (CCM). These mechanisms give all agents the possibility to condition their contribution on the total level of contribution provided by all agents. Their dynamic incentive structure makes the CCMs particularly suited for repeated public goods. I prove for a very general class of environments that all equilibria of the CCMs under a new variant of Better Response Dynamics, called Unexploitable Better Response Dynamics (UBRD), are Pareto efficient. I further present a first experimental study of one mechanism's performance compared to the performance of the Voluntary Contribution Mechanism. I find that a significantly higher contribution rate can be observed when the CCM is used. Furthermore, all stable outcomes of the CCM, which are observed in the experiment, are in line with the prediction of UBRD.

ABSTRACT. The experimental evidence suggests that groups are inefficient at providing threshold public goods. This inefficiency appears to reflect an inability to coordinate over how to distribute the cost of providing the good. So, why do groups not just split the cost equally? We offer an answer to this question by demonstrating that in a standard threshold public good game there is no collectively rational recommendation. We also demonstrate that if full agreement is required in order to provide the public good then there is a collectively rational recommendation, namely, to split the cost equally. Requiring full agreement may, therefore, increase efficiency in providing threshold public goods. We test this hypothesis experimentally and find support for it.

ABSTRACT. How can managers in organizations utilize asymmetric information among workers to motivate them in a competition? We consider the information disclosure policy of the manager as a contest designer in an all-pay auction, where one competitor's ability is public information, and the other competitor's ability is private information. In order to optimally motivate the contestants, the manager will reveal the private information of the unknown competitor when the publicly known competitor's ability is sufficiently low. The information asymmetry among contestants creates a tradeoff between ability-based advantage, and information-based advantage, which managers can invoke when attempting to maximize the total effort of competing employees. However, in the case where the private competitor's ability is not directly verifiable, an incentive problem may exist when enforcing the disclosure or concealment policy.

ABSTRACT. In a multi-battle contest, each time a player competes by investing some of her budget in a component battle to collect a value if winning the battle. There are multiple battles to fight, and the budget gets consumed over time. The final winner in the overall contest is the one who first reaches some amount of total value. Examples include R & D races, sports competition, elections, and many more.

We model such budget-constrained contests as zero-sum games where each component battle is a first-price or all-pay auction. We focus on analyzing the 2-player budget ratio that guarantees the winning of the player under study against the other omnipotent player. In various settings, we give efficient dynamic programs to find the optimal budget ratios and the corresponding bidding strategies. Our definition of games, budget constraints, and emphasis on budget analyses provide a new perspective and analysis in the related context.

ABSTRACT. We consider a two-player rent-seeking contest for a prize of common value. The players only know that the prize is high or low, with given probabilities. Each player can hire a delegate to act on his behalf. After a delegate is hired, she privately observes the true value of the prize. In this setup, we demonstrate that delegation can occur in equilibrium. We derive the conditions under which, respectively no player, only one player, or both players delegate in equilibrium.

ABSTRACT. This paper formalizes the idea that experts enjoy exerting influence and explores its implications for experts' communication (e.g. policy and financial advice). An expert who enjoys exerting influence benefits from inducing a client's action which differs from the client's action in absence of expertise. We find that influence tempts the expert to exaggerate the observed state and send messages far from the client's ex-ante optimal action (in absence of expertise). The incentive to exaggerate is stronger, the further away is the state from the client's ex-ante optimal action. When communication is truthful, the expert's incentive to exaggerate translates into less accurate communication. Messages close the client's ex-ante optimal action are hence more informative than messages far from it. In an extension we also consider the case in which the client enjoys being influenced.

ABSTRACT. Kamenica and Gentzkow (2011) consider a model in which a sender chooses a public communication device for signaling his information to an uninformed receiver, who then takes an action that affects the welfare of both individuals. In their model, the sender is fully committed to truthfully communicate the signal to the receiver, so that they abstract from incentive compatibility issues. By considering mediated communication, we provide an analytical framework overcoming this overly restrictive assumption. We use the concept of virtual utility to develop a geometric approach to the sender's optimization problem. We characterize the optimal value of persuasion from the concavication of a virtual non-revealing function over beliefs. We apply our approach to a model of information transmission based on Crawford and Sobel (1982). We provide necessary and sufficient conditions for the sender to benefit from his private information.

ABSTRACT. We introduce contractible participation into a multiple-expert persuasion game. Prior to persuasion, communication has to be approved by both the decision-maker and the expert in a bilateral transaction. We analyze a trading protocol in which the decision-maker is a discriminating price-setter and a protocol in which the decision-maker is a price-taker. For both protocols, we identify necessary equilibrium conditions in the form of signs of appropriately constructed bilateral surpluses. We construct the surpluses for ex ante transactions (transactions before experts learn evidence) in general and for interim transactions (transactions after experts learn evidence) in the case of binary independent signals. We identify when the surplus underestimates or overestimates bilateral and multilateral efficiency of the transaction. We also apply surpluses to find substitutable and complementary pairs of transactions.

ABSTRACT. The goal of the present paper is to analyze the optimal targeting strategies of a planner (say a monopolist) who aims to increase the aggregate action of agents (consumers' purchase). Agents are embedded in a social network and their actions influence each other. Actions are complements, determined by their exposure to neighbors's actions through a response function. The description includes strategic settings and models of mechanical influence as in contagion or mimesis. When the response function is linear, the optimal targeting strategies are explicit, characterized by well-known centralities indices. When the response function is not linear, concave or convex, new features pertaining to the pattern of the agents' attention and the joint impact between pairs determine the optimal targeting. The value of information on the impact structure is shown to be (almost always) positive and related to some form of heterogeneity between agents.

ABSTRACT. We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing game between the sellers. We prove positive and negative results, both of ``Price of Anarchy'' and of ``Price of Stability'' type, for simple graphs (lines, cycles) as well as more general ones (trees, graphs). We describe best-reply dynamics that converge to non-trivial equilibrium in several families of graphs, and we use these dynamics to prove the existence of approximately-efficient equilibria.

ABSTRACT. We consider a Hotelling game where a finite number of retailers choose a location, given that their potential consumers are distributed on a network. Retailers compete only on location, therefore each consumer shops at the closest store. We show that when the number of retailers is large enough, the game admits a pure Nash equilibrium and we construct it. We then compare the equilibrium cost borne by the consumers with the cost that could be achieved if the retailers followed the dictate of a benevolent planner. We perform this comparison in term of the induced price of anarchy, i.e., the ratio of the worst equilibrium cost and the optimal cost, and the induced price of stability, i.e., the ratio of the best equilibrium cost and the optimal cost. We show that, asymptotically in the number of retailers, these ratios are two and one, respectively.

ABSTRACT. We study Equilibria under Ambiguity (EUA) with optimism and pessimism as introduced in Eichberger & Kelsey (2014) for the case of beliefs modelled by belief functions. We show existence of equilibria for finite games with an arbitrary number of players and both general and specific ambiguity about the opponents' strategy choice. We illustrate by examples the potential of this approach to model behavior which cannot be obtained as a Nash equilibrium.

ABSTRACT. We introduce a strategic game model with ambiguity as follows: each player fears some possible modification of the expected strategies of the other players (for example because they are not sure of the rationality of the other players), and has a pessimistic behaviour. But each player can insure himself against such modifications, the level of insurance being related to ambiguity. The main results of the paper are 1) The insurance and the pessimistic behaviour of each player has a "smoothing effect", and entails the existence of a Nash equilibrium under weak assumptions 2) When the level of insurance goes to 0, we get maxmin equilibria at the limit 3) When the level of insurance goes to infinity, we get Nash equilibria of standard strategic games (without pessimistic behaviour), even in large classes of discontinuous games as better-reply secure games. Technically, the smoothing effect described below is related to Moreau-Yosida regularization.

ABSTRACT. In many common interactive scenarios, participants lack information about other participants, and specifically about the preferences of other participants. In this work, we model an extreme case of information absence we term type-ambiguity: when a participant lacks information enabling him to form a belief on the preferences of others. Under type-ambiguity, one cannot analyze the scenario using the Bayesian framework, and needs to model participants using a different decision model.
We present the MINthenMAX decision model under ambiguity. This model is a refinement of Wald’s MiniMax principle, which we show to be too coarse. We characterize MINthenMAX as the finest refinement of the MiniMax principle that satisfies properties we claim are necessary for games with type-ambiguity. Finally, we define and analyze the corresponding equilibrium concept when all players follow MINthenMAX. We demonstrate this equilibrium by applying it to two common economic scenarios: Coordination games and Bilateral trade.

ABSTRACT. In the literature on static and dynamic games, most rationalizability concepts have an equilibrium counterpart. In two-player games, the equilibrium counterpart is obtained by taking the epistemic conditions of the rationalizability concept and adding the following correct beliefs assumption: (a) each player believes that the opponent is correct about his beliefs, and (b) each player believes that the opponent believes that he is correct about the opponent's beliefs. This paper shows that there is no equilibrium counterpart to the forward induction concept of extensive-form rationalizability (Pearce (1984), Battigalli (1997)), epistemically characterized by common strong belief in rationality (Battigalli and Siniscalchi (2002)). The reason is that there are games where the epistemic conditions of common strong belief in rationality are logically inconsistent with the correct beliefs assumption. In fact, we show that this inconsistency holds for "most" dynamic games of interest.

ABSTRACT. We bring together two ideas: rationalizability in the extensive form (Pearce, 1984) and invariance-the notion that the solution of a game in extensive form should be invariant under any equivalence transformation of that extensive form. We focus on a particular class of equivalence transformations: those that leave the associated reduced normal form unchanged. We show that rationalizability in the extensive form can be decomposed into a process that operates on families of truncations of the associated reduced normal form. We demonstrate that rationalizability in the extensive form is invariant under interchange of simultaneous moves and coalescing of moves, but that it is not invariant under addition of a superfluous move. Yet, for a given reduced normal form, there exists a set of strategy profiles that is contained in the set of extensive-form rationalizable strategy profiles of any extensive form that has that reduced normal form: the invariant extensive-form rationalizable set.

ABSTRACT. In this paper we define minimum cost spanning tree problems with multiple sources. We extend the different definitions of the folk rule, defined for classical minimum cost spanning tree problems, to this new context.

ABSTRACT. We consider an environment in which several service providers with possibly criticality differences can collaborate by pooling their spare parts. Every collaborating group of service providers uses a critical level policy that focusses on the long-term average cost. We examine the allocation of the collective cost savings for such pooled situation by studying an associated cooperative game, which we call a criticality game. We analyze various properties of these criticality games.

ABSTRACT. A highway problem is a cost sharing problem that arises if each player demands consecutive sections of a common resource. We show that the core, the prenucleolus, and the Shapley value on the arising class of TU highway games possess characterizations by intuitive properties formulated without referring to the associated games. The main axioms for the core and nucleolus are consistency properties, related to traditional axioms, on reduced highway problems that arise by eliminating a player and using her charge to maintain a certain part of her sections. The Shapley value is characterized either using individual independence of outside changes or using the new contraction property. Together with the axiom of aggregating the shares of all agents of any player, the axiomatizations of the core and the value may be expanded to generalized highway problems (the associated games are positive and vice versa) in which players may demand non-connected parts.

ABSTRACT. We examine whether and how democratic procedures can achieve socially desirable public good provision in the presence of profound uncertainty about benefits of public goods, i.e., when citizens are able to identify the distribution of benefits only if they aggregate their private information. Some members of the society, however, are harmed by socially desirable policies and aim at manipulating information aggregation by misrepresenting their private information. We show that information can be aggregated and a socially desirable policy can be implemented under a new class of democratic mechanisms involving a sample group. These mechanisms reflect the principles of liberal democracy, are procedurally efficient, and involve a conditional tax privilege of sample group members. This tax treatment motivates sample group members to reveal private information truthfully before voting takes place. Depending on the distance between two feasible public good levels, the optimal mechanism involves either one or two voting rounds.

ABSTRACT. This paper studies decentralized vote trading in a power-sharing framework that follows the rules of strategic market games. In particular we study a two-party election, in which prior to the voting stage voters are free to trade votes for money. Voters hold private information about both their ordinal and cardinal preferences, whereas their utilities are proportionally increasing in the vote-share of their favorite party. In this framework we prove generic existence of a unique full trade equilibrium (an equilibrium in which nobody refrains from vote trading). We moreover argue that vote trading in such systems unambiguously improves voters' welfare.

ABSTRACT. Can a team of non-communication agents coordinate so as to achieve some common goal? Earlier approaches have centred on rendezvous search (where the goal is meeting) and spatial dispersion (with the opposite goal). Here we study how they can best amalgamate their private information about a binary state of Nature. The agents are heterogeneous in their ability, the quality of their private information. They cannot possibly to directly communicate their information, but instead can only vote between the two states. We first describe possible methods of sequential majority voting and then analyse a particular one: The first n-1 jurors vote simultaneously and, in the case of a tie, the remaining juror has the casting vote. We prove that when n = 3 (a common situation for a tribunal of three judges), the probability of a correct verdict is maximized when the agent of median ability has the casting vote.

ABSTRACT. We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that _smooth calibration_ can be guaranteed by _deterministic_ procedures. As a consequence, it does not matter if the forecasts are _leaked_, i.e., made known in advance: smooth calibration can nevertheless be guaranteed (while regular calibration cannot). Moreover, our procedure has _finite recall_, is stationary, and all forecasts lie on a finite grid. We also consider related problems: online linear regression, weak calibration, and uncoupled Nash dynamics in n-person games that result from smooth calibrated learning.

ABSTRACT. Forecasters' are routinely evaluated using statistical tests. This creates an incentive for forecasters to strategically distort their predictions in an effort to appear knowledgeable. A growing literature has shown the manipulative effects of these incentives: most known statistical tests are ineffective at discriminating between forecasters who are knowledgeable and forecasters who are uninformed but strategic. This adverse selection problem can be solved by restricting the domain of permissible forecasts. This paper provides sufficient and necessary conditions under which a domain of permissible forecasts can be effectively tested. These conditions have a natural Bayesian interpretation. The result subsumes different existing contributions in the literature. It follows from the result that it is without loss of generality to restrict the attention to standard likelihood-ratio tests. In addition, it provides a novel connection between the problem of testing strategic forecasters, Bayesian statistics, and the classical Neyman-Pearson paradigm.