Working Papers
By Year:
Paper #  Author  Title  

16018 
George J. Mailath Stephen Morris Andrew Postlewaite 
Laws and Authority  
A law prohibiting a particular behavior does not directly change the payoff to an individual should he engage in the prohibited behavior. Rather, any change in the individual’s payoff, should he engage in the prohibited behavior, is a consequence of changes in other peoples’ behavior. If laws do not directly change payoffs, they are “cheap talk,” and can only affect behavior because people have coordinated beliefs about the effects of the law. Beginning from this point of view, we provide definitions of authority in a variety of problems, and investigate how and when individuals can have, gain, and lose authority. Download Paper


16013 
Venkataraman Bhaskar George J. Mailath 
The Curse of Long Horizons  
We study dynamic moral hazard with symmetric ex ante uncertainty about the difficulty of the job. The principal and agent update their beliefs about the difficulty as they observe output. Effort is private and the principal can only offer spot contracts. The agent has an additional incentive to shirk beyond the disutility of effort when the principal induces effort: shirking results in the principal having incorrect beliefs. We show that the effort inducing contract must provide
increasingly high powered incentives as the length of the relationship increases. Thus it is never optimal to always induce effort in very long relationships. Download Paper


15034 
George J. Mailath Andrew Postlewaite Larry Samuelson 
Premuneration Values and Investments in Matching Markets  
We analyze a model in which agents make investments and then match into pairs to create a surplus. The agents can make transfers to reallocate their pretransfer ownership claims on the surplus. Mailath, Postlewaite, and Samuelson (2013) showed that when investments are unobservable, equilibrium investments are generally inefficient. In this paper we work with a more structured model that is sufficiently tractable to analyze the nature of the investment inefficiencies. We provide conditions under which investment is inefficiently high or low and conditions under which changes in the pretransfer ownership claims on the surplus will be Pareto improving, as well as examine how the degree of heterogeneity on either side of the market affects investment efficiency. Download Paper


15012 
George J. Mailath Andrew Postlewaite Larry Samuelson 
"Buying Locally"  
“Buy local” arrangements encourage members of a community or group to patronize one another rather than the external economy. They range from formal mechanisms such as local currencies to informal “I’ll buy from you if you buy from me” arrangements, and are often championed on social or environmental grounds. We show that in a monopolistically competitive economy, buy local arrangements can have salutary effects even for selfish agents immune to social or environmental considerations. Buy local arrangements effectively allow firms to exploit the equilibrium pricecost gap to profitably expand their sales at the going price. Download Paper


15008 
George J. Mailath Volker Nocke Lucy White 
"When and How the Punishment Must Fit the Crime"  
In repeated normalform (simultaneousmove) games, simple penal codes (Abreu, 1986, 1988) permit an elegant characterization of the set of subgameperfect outcomes. We show that the logic of simple penal codes fails in repeated extensiveform games. By means of examples, we identify two types of settings in which a subgameperfect outcome may be supported only by a profile with the property that the continuation play after a deviation is tailored not only to the identity of the deviator, but also to the nature of the deviation. Download Paper


13060 
George J. Mailath Andrew Postlewaite Larry Samuelson 
"Premuneration Values and Investments in Matching Markets"  
We analyze a model in which agents make investments and then match into pairs to create a surplus. The agents can make transfers to reallocate their pretransfer ownership claims on the surplus. Mailath, Postlewaite, and Samuelson (2013) showed that when investments are unobservable, equilibrium investments are generally inefficient. In this paper we work with a more structured model that is sufficiently tractable to analyze the nature of the investment inefficiencies. We provide conditions under which investment is inefficiently high or low and conditions under which changes in the pretransfer ownership claims on the surplus will be Pareto improving, as well as examine how the degree of heterogeneity on either side of the market affects investment efficiency. Download Paper


13044 
George J. Mailath Larry Samuelson 
"Reputations in Repeated Games", Second Version  
This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in repeated games of incomplete information. Download Paper


13034 
George J. Mailath Larry Samuelson 
"Reputations in Repeated Games"  
This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in repeated games of incomplete information. Download Paper


13028 
Qingmin Liu George J. Mailath Andrew Postlewaite Larry Samuelson 
"Stable Matching with Incomplete Information, Second Version"  
We formulate a notion of stable outcomes in matching problems with onesided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make. We show that the set of stable outcomes is nonempty in incompleteinformation environments, and is a superset of the set of completeinformation stable outcomes. We then provide sufficient conditions for incompleteinformation stable matchings to be efficient. Lastly, we define a notion of pricesustainable allocations and show that the set of incompleteinformation stable matchings is a subset of the set of such allocations. Download Paper


12043 
V. Bhaskar George J. Mailath Stephen Morris 
"A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games"  
We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical noncooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents' payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player's strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one longrun player, all purifiable equilibria are Markov. Download Paper


12042 
Qingmin Liu George J. Mailath Andrew Postlewaite Larry Samuelson 
"Stable Matching with Incomplete Information", Second Version  
We formulate a notion of stable outcomes in matching problems with onesided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable. We show that the set of stable outcomes is nonempty in incomplete information environments, and is a superset of the set of completeinformation stable outcomes. We then provide sufficient conditions for incompleteinformation stable matchings to be efficient. Lastly, we define a notion of price sustainable allocations and show that the set of incomplete information stable matchings is a subset of the set of such allocations. Download Paper


12032 
Qingmin Liu George J. Mailath Andrew Postlewaite Larry Samuelson 
"Matching with Incomplete Information"  
A large literature uses matching models to analyze markets with twosided heterogeneity, studying problems such as the matching of students to schools, residents to hospitals, husbands to wives, and workers to firms. The analysis typically assumes that the agents have complete information, and examines core outcomes. We formulate a notion of stable outcomes in matching problems with onesided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable. We show that the set of stable outcomes is nonempty in incomplete information environments, and is a superset of the set of completeinformation stable outcomes. We provide sufficient conditions for incompleteinformation stable matchings to be efficient. Download Paper


12008 
George J. Mailath Andrew Postlewaite Larry Samuelson 
“Premuneration Values and Investments in Matching Markets”  
We examine markets in which agents make investments and then match into pairs, creating surpluses that depend on their investments and that can be split between the matched agents. In general, each of the matched agents would ”own" part of the surplus in the absence of interagent transfers. Most of the work in the large bargainingand matching literature ignores this initial ownership of the surplus. We show that when investments are not observable to potential partners, initial ownership affects the efficiency of equilibrium investments and affects the agents' payoffs. In particular, it is possible that reallocating initial ownership could increase welfare on both sides of the match. Download Paper


12003 
V. Bhaskar George J. Mailath Stephen Morris 
“A Foundation for Markov Equilibria with Finite Social Memory”  
We study stochastic games with an infinite horizon and sequential moves played by an arbitrary number of players. We assume that social memory is finiteevery player, except possibly one, is finitely lived and cannot observe events that are sufficiently far back in the past. This class of games includes games between a longrun player and a sequence of shortrun players and games with overlapping generations of players. Indeed, any stochastic game with infinitely lived players can be reinterpreted as one with finitely lived players: Each finitelylived player is replaced by a successor, and receives the value of the successor's payoff. This value may arise from altruism, but the player also receives such a value if he can “sell” his position in a competitive market. In both cases, his objective will be to maximize infinite horizon payoffs, though his information on past events will be limited. An equilibrium is purifiable if closeby behavior is consistent with equilibrium when agents' payoffs in each period are perturbed additively and independently. We show that only Markov equilibria are purifiable when social memory is finite. Thus if a game has at most one longrun player, all purifiable equilibria are Markov. Download Paper


11012 
Martin W. Cripps Jeffrey C. Ely George J. Mailath Larry Samuelson 
"Common Learning with Intertemporal Dependence"  
Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. Will the agents commonly learn the value of the parameter, i.e., will the true value of the parameter become approximate commonknowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps, Ely, Mailath, and Samuelson, 2008). This paper explores the implications of allowing the signals to be dependent over time. We present a counterexample showing that even extremely simple time dependence can preclude common learning, and present sufficient conditions for common learning. Download Paper


10037 
George J. Mailath Andrew Postlewaite Larry Samuelson 
"Pricing and Investments in Matching Markets", Second Version  
Different markets are cleared by different types of pricessellerspecific prices that are uniform across buyers in some markets, and personalized prices tailored to the buyer in others. We examine a setting in which buyers and sellers make investments before matching in a competitive market. We introduce the notion of premuneration valuesthe values to the transacting agents prior to any transferscreated by a buyerseller match. Personalized price equilibrium outcomes are independent of premuneration values and exhibit inefficiencies only in the event of "coordination failures," while uniformprice equilibria depend on premuneration values and in general feature inefficient investments even without coordination failures. There is thus a tradeoff between the costs of personalizing prices and the inefficient investments under uniform prices. We characterize the premuneration values under which uniformprice equilibria similarly exhibit inefficiencies only in the event of coordination failures. Download Paper


10032 
George J. Mailath ErnestLudwig Thadden 
"Incentive Compatibility and Differentiability: New Results and Classic Applications"  
This note provides several generalizations of Mailath's (1987) result that incentive compatibility plus separation implies differentiability. The new results extend the theory to classic models in finance such as Leland and Pyle (1977), Glosten (1989), and De Marzo and Duffie (1999), that were not previously covered. Download Paper


10007 
George J. Mailath Wojciech Olszewski 
"Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring", Third Version  
We prove the perfectmonitoring folk theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. As a consequence, the perfect monitoring folk theorem is shown to be behaviorally robust under almostperfect almostpublic monitoring. That is, the same specification of behavior continues to be an equilibrium when the monitoring is perturbed from perfect to highlycorrelated private. Download Paper


10003 
George J. Mailath Andrew Postlewaite Larry Samuelson 
"Pricing in Matching Markets"  
Different markets are cleared by different types of pricesa universal price for all buyers and sellers in some markets, sellerspecific prices that are uniform across buyers in others, and personalized prices tailored to both the buyer and the seller in yet others. We introduce the notion of premuneration valuesthe values in the absence of any muneration (payments)created by the buyerseller match. We characterize the premuneration values under which uniformprice and personalizedprice equilibria agree. In this case, we have efficient allocations, including prematch investment decisions, without the costs of personalized pricing. We then examine the inefficiencies that arise when the premuneration values preclude the agreement of uniformprice and personalizedprice equilibria. We view premuneration values as an important consideration in market design. Download Paper


09029 
V. Bhaskar George J. Mailath Stephen Morris 
"A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games"  
We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical noncooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents' payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player's strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one longrun player, all purifiable equilibria are Markov. Download Paper


08027 
George J. Mailath Wojciech Olszewski 
"Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring", Second Version  
A strategy profile in a repeated game has bounded recall L if play under the profile after two distinct histories that agree in the last L periods is equal. Mailath and Morris (2002, 2006) proved that any strict equilibrium in boundedrecall strategies of a game with full support public monitoring is robust to all perturbations of the monitoring structure towards private monitoring (the case of almostpublic monitoring), while strict equilibria in unboundedrecall strategies are typically not robust. We prove the perfectmonitoring folk theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. As a consequence, the perfect monitoring folk theorem is shown to be behaviorally robust under almostperfect almostpublic monitoring. That is, the same specification of behavior continues to be an equilibrium when the monitoring is perturbed from perfect to highlycorrelated private. Download Paper


08019 
George J. Mailath Wojciech Olszewski 
"Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring"  
A strategy profile in a repeated game has L bounded recall if play under the profile after two distinct histories that agree in the last L periods is equal. Mailath and Morris (2002, 2006) proved that any strict equilibrium in boundedrecall strategies of a game with full support public monitoring is robust to all perturbations of the monitoring structure towards private monitoring (the case of "almostpublic monitoring"), while strict equilibria in unboundedrecall strategies are typically not robust. We prove that the perfectmonitoring folk theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. The general result uses calendar time in an integral way in the construction of the strategy profile. If the players' action spaces are sufficiently rich, then the strategy profile can be chosen to be independent of calendar time. Either result can then be used to prove a folk theorem for repeated games with almostperfect almostpublic monitoring. Download Paper


07034 
George J. Mailath 
"Reputation Effects"  
This article gives a brief introduction to reputation effects. A canonical model is described, the reputation bound result of Fudenberg and Levine (1989 1992) and the temporary reputation result of Cripps, Mailath, and Samuelson (2004, 2007) are stated and discussed. Download Paper


07024 
V. Bhaskar George J. Mailath Stephen Morris 
"Purification in the InfinitelyRepeated Prisoners' Dilemma", Second Version  
This paper investigates the Harsanyi (1973)purifiability of mixed strategies in the repeated prisoners’ dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of oneperiod memory mixed strategy equilibria used by Ely and Välimäki (2002) in their study of the repeated prisoners’ dilemma with private monitoring. We find that any such strategy profile is not the limit of oneperiod memory quilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completelymixed equilibrium is purifiable. Download Paper


07022 
George J. Mailath Georg Noldeke 
"Does Competitive Pricing Cause Market Breakdown under Extreme Adverse Selection?"  
We study market breakdown in a finance context under extreme adverse selection with and without competitive pricing. Adverse selection is extreme if for any price there are informed agent types with whom uninformed agents prefer not to trade. Market breakdown occurs when no trade is the only equilibrium outcome. We present a necessary and sufficient condition for market breakdown. If the condition holds, then trade is not viable. If the condition fails, then trade can occur under competitive pricing. There are environments in which the condition holds and others in which it fails. Download Paper


07018 
Martin W. Cripps Jeffrey C. Ely George J. Mailath Larry Samuelson 
"Common Learning"  
Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate commonknowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case. Download Paper


06003 
George J. Mailath Andrew Postlewaite 
"Social Assets", Third Version  
We present a model incorporating both social and economic components, and analyze their interaction. The notion of a social asset, an attribute that has value only because of the social institutions governing society, is introduced. In the basic model, agents match on the basis of income and unproductive attributes. An attribute has value in some equilibrium social institutions (matching patterns), but not in others. We then show that productive attributes (such as education) can have their value increased above their inherent productive value by some social institutions, leading to the notion of the social value of an asset. Download Paper


05014 
George J. Mailath Stephen Morris 
"Coordination Failure in Repeated Games with AlmostPublic Monitoring", Second Version  
Some privatemonitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games with general almostpublic private monitoring, this is essentially the only behavior that can coordinate continuation play. Download Paper


04039 
George J. Mailath Volker Nocke Lucy White 
"When the Punishment Must Fit the Crime: Remarks on the Failure of Simple Penal Codes in ExtensiveForm Games"  
In repeated normalform games, simple penal codes (Abreu 1986, 1988) permit an elegant characterization of the set of subgameperfect outcomes. We show that the logic of simple penal codes fails in repeated extensiveform games. We provide two examples illustrating that a subgameperfect outcome may be supported only by a profile with the property that the continuation play after a deviation is tailored not only to the identity of the deviator, but also to the nature of the deviation. Download Paper


04033 
George J. Mailath Stephen Morris 
"Coordination Failure in Repeated Games with AlmostPublic Monitoring"  
Some privatemonitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing publicmonitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficent to determine behavior). We show that, in games with general almostpublic private monitoring, this is essentially the only behavior that can coordinate continuation play. Download Paper


04031 
Martin W. Cripps George J. Mailath Larry Samuelson 
"Disappearing Private Reputations in LongRun Relationships", Second Version  
For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps, Mailath, and Samuelson (2004) showed that an informed player facing shortlived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is longlived and has private beliefs, so that the informed player's reputation is private. We also show that the rate at which reputations disappear is uniform across equilibria and that reputations disappear in sufficiently long discounted finitelyrepeated. Download Paper


04025 
George J. Mailath Andrew Postlewaite 
"Social Assets", Second Version  
We present a model incorporating both social and economic components, and analyze their interaction. The notion of a social asset, an attribute that has value only because of the social institutions governing society, is introduced. In the basic model, agents match on the basis of income and unproductive attributes. An attribute has value in some equilibrium social institutions (matching patterns), but not in others. We then show that productive attributes (such as education) can have their value increased above their inherent productive value by some social institutions, leading to the notion of the social value of an asset. Download Paper


04008 
Martin W. Cripps George J. Mailath Larry Samuelson 
"Disappearing Private Reputations in LongRun Relationships"  
For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps, Mailath, and Samuelson (2004) showed that an informed player facing shortlived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is longlived and has private beliefs, so that the informed player's reputation is private. Download Paper


04007 
George J. Mailath Andrew Postlewaite Larry Samuelson 
"Sunk Investments Lead to Unpredictable Prices", Second Version  
We study transactions that require investments before trading in a competitive market, when forward contracts fixing the transaction price are absent. We show that, despite the market being perfectly competitive and subject to arbitrarily little uncertainty, the inability to jointly determine investment levels and prices may make it impossible for buyers and sellers to predict the prices at which they will trade, leading to inefficient levels of investment and trade. Download Paper


04004 
V. Bhaskar George J. Mailath Stephen Morris 
"Purification in the InfinitelyRepeated Prisoners' Dilemma"  
This paper investigates the Harsanyi (1973)purifiability of mixed strategies in the repeated prisoners' dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of a class of oneperiod memory mixed strategy equilibria used by Ely and Välimäki (2002) in their study of the repeated prisoners' dilemma with private monitoring. We find that the strategy profile is purifiable by perturbedgame finitememory strategies if and only if it is strongly symmetric, in the sense that after every history, both players play the same mixed action. Thus "most" strategy profiles are not purifiable by finite memory strategies. However, if we allow infinite memory strategies in the perturbed game, then any completelymixed equilibrium is purifiable. Download Paper
