We analyse efficient risk-sharing arrangements when the value from deviating is determined endogenously by another risk-sharing arrangement. Coalitions form to insure against idiosyncratic income risk. Self-enforcing contracts for both the original coalition and any coalition formed (joined) after deviations rely on a belief in future cooperation which we term "trust". We treat the contracting conditions of original and deviation coalitions symmetrically and show that higher trust tightens incentive constraints since it facilitates the formation of deviating coalitions. As a consequence, although trust facilitates the initial formation of coalitions, the extent of risk sharing in successfully formed coalitions is declining in the extent of trust and efficient allocations might feature resource burning or utility burning: trust is indeed a double-edged sword.

We analyze efficient risk-sharing arrangements when coalitions may deviate. Coalitions form to insure against idiosyncratic income risk. Self-enforcing contracts for both the original coalition and any deviating coalition rely on a belief in future cooperation which we term “social capital”. We treat the contracting conditions of original and deviating coalitions symmetrically and show that higher social capital tightens incentive constraints since it facilitates both the formation of the original as well as a deviating coalition. As a consequence, although social capital facilitates the initial formation of coalitions, the extent of risk sharing in successfully formed coalitions is declining in the extent of social capital and equilibrium allocations might feature resource burning or utility burning: social capital is indeed a double-edged sword.

I study the design of dynamic certification for firms that are privately informed about their competence and their efforts towards quality provision. I show that an honors scheme maximizes the certifier’s revenue; at each time, a competent firm is either “certified” or “certified with honors.” The scheme has a low standard: an inept firm is always “certified.” To maximize revenue, the certifier uses the “certified” rating to transfer some surplus from competent firms to inept firms. The results highlight the certifier’s trade-off of screening a firm’s competence and providing incentives for high effort, and address concerns about certification in practice.

People reason about uncertainty with deliberately incomplete models. How do people hampered by different, incomplete views of the world learn from each other? We introduce a model of “ model-based inference.” Model-based reasoners partition an otherwise hopelessly complex state space into a manageable model. Unless the differences in agents’ models are trivial, interactions will often not lead agents to have common beliefs or beliefs near the correct-model belief. If the agents’ models have enough in common, then interacting will lead agents to similar beliefs, even if their models also exhibit some bizarre idiosyncrasies and their information is widely dispersed. (JEL D82, D83)

“Crowds” are often regarded as “wiser” than individuals, and prediction markets are often regarded as effective methods for harnessing this wisdom. If the agents in prediction markets are Bayesians who share a common model and prior belief, then the no-trade theorem implies that we should see no trade in the market. But if the agents in the market are not Bayesians who share a common model and prior belief, then it is no longer obvious that the market outcome aggregates or conveys information. In this paper, we examine a stylized prediction market comprised of Bayesian agents whose inferences are based on different models of the underlying environment. We explore a basic tension—the differences in models that give rise to the possibility of trade generally preclude the possibility of perfect information aggregation.

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.

It is impossible to understand modern economics without knowledge of the basic tools of gametheory and mechanism design. This book provides a graduate-level introduction to the economic modeling of strategic behavior. The goal is to teach Economics doctoral students the tools of game theory and mechanism design that all economists should know.

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.

In repeated normal-form (simultaneous-move) games, simple penal codes (Abreu, 1986, 1988) permit an elegant characterization of the set of subgame-perfect outcomes. We show that the logic of simple penal codes fails in repeated extensive-form games. By means of examples, we identify two types of settings in which a subgame-perfect 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.

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.

We analyze efficient arrangement of financial coalitions under incomplete enforcement, which are endogenously formed to undertake consumption smoothing and joint investment. We explicitly consider the symmetric contracting conditions of the individuals who seek to deviate from the contract with the initial contracting conditions, by considering the possibility that they can construct deviating coalitions. The self-enforcing contracts for both the original coalition and any deviating coalition rely on the belief in future cooperation and thus we investigate the role of belief coordination on endogenous formation and activities of financial institutions to show both beneficial and harmful effects. The real return on the joint investment can also play both positive and negative role in these symmetric contracting environments. We examine the extent to which the belief coordination and real returns are substitutes or complements, and their implications about self-enforcing arrangements.

Buy local arrangements encourage members of a community or group to patronize one another instead of 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 price-cost gap to profitably expand their sales at the going price.

“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 price-cost gap to profitably expand their sales at the going price.

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.

This paper surveys work on reputations in repeated games of incomplete information. We first develop the adverse-selection approach to reputations in the context of a long-lived player, who may be a “normal” type or one of a number of “commitment” types, and who faces a succession of short-lived players. We use entropy-based arguments both to establish a lower bound on the equilibrium payoff of the long-lived player (demonstrating ex ante reputation effects) and to show that this lower bound is asymptotically irrelevant under imperfect monitoring (demonstrating the impermanence of reputation effects). The chapter continues by examining the (necessarily weaker) reputation results that can be established for the case of two long-lived players, and by examining variations in the model under which reputation effects can persist indefinitely. The chapter closes with brief remarks on alternative approaches.

We formulate a notion of stable outcomes in matching problems with one-sided 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 complete-information stable outcomes. We then provide sufficient conditions for incomplete-information 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.

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.

We study stochastic games with an infinite horizon and sequential moves played by an arbitrary number of players. We assume that social memory is finite every 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 long-run player and a sequence of short-run 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 finitely lived 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 close-by 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 long-run player, all purifiable equilibria are Markov.

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 common-knowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps et al., Econometrica, 76(4):909–933, 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.