Uniform Folk Theorems in Repeated Anonymous Random Matching Games

We study infinitely repeated anonymous random matching games played by communities of players, who only observe the outcomes of their own matches. It is well known that cooperation can be sustained in equilibrium for the prisoner’s dilemma (PD) through grim trigger strategies. Little is known about games beyond the PD. We study a new equilibrium concept, strongly uniform equilibrium (SUE, which refines the notion of uniform equilibrium (UE) and has additional properties such as a strong version of (approximate) sequential rationality. We establish folk theorems for general games and arbitrary number of communities. Interestingly, the equilibrium strategies we construct are easy to play. We extend the results to a setting with imperfect private monitoring, for the case of two communities. We also show that it is possible for some players to get equilibrium payoffs that are outside the set of individually rational and feasible payoffs of the stage game. In particular, for the PD we derive a bound on the number of “free-riders” that can be sustained in society. A by-product of our analysis is an important result relating uniform equilibrium and strongly uniform equilibria: we show that, in general repeated games with finite players, actions, and signals, the set of UE and SUE payoffs coincide

A Minority Game with Bounded Recall

International audienceThis paper studies a repeated minority game with public signals, symmetric bounded recall and pure strategies. We investigate both public and private equilibria of the game with fixed recall size. We first show how public equilibria in such repeated games can be represented as colored sub-graphs of a de Bruijn graphs. Then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases. We also show that private equilibria behave badly: a private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff

Discounted and finitely repeated minority games with public signals

We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a nitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payos Hausdor-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to innity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a nitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payos Hausdor-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to innity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.Refereed Working Papers / of international relevanc

Essays on Information Economics

This dissertation consists of three independent essays that examine how to improveinformation transmission and how to incentivize learning. In Chapter 2, I study the role of a recommender’s career concerns in his relation-ship with a consumer when the recommender has a private type in expertise. An informed type has valuable expertise for the consumer, whereas an uninformed type does not. The uninformed type cannot mimic the informed type, suggesting that the informed type can build a reputation for competence. However, I find that the relationship breaks down completely if the recommender is sufficiently patient. In Chapter 3, which is co-authored with Florian Ederer, we embed probabilisticlie detection in a standard model of Bayesian persuasion. We show that the Sender lies more when the lie detection probability increases. Moreover, the Sender’s and the Receiver’s equilibrium payoffs are unaffected by a weak lie detection technology because the Sender compensates by lying more. In Chapter 4, I analyze optimal contracting for experimentation when the agent who experiments and the principal who provides incentives agree to disagree over the quality of the project. If efforts are contractible, the principal prefers to reward good outcomes (efforts) exclusively for a more (less) optimistic agent. Moreover, longer experimentation is sustained with non-common prior. If efforts are not contractible, the optimal duration of experimentation is increasing in the agent’s confidence

Essays on Information Economics

This dissertation consists of three independent essays that examine how to improveinformation transmission and how to incentivize learning. In Chapter 2, I study the role of a recommender’s career concerns in his relation-ship with a consumer when the recommender has a private type in expertise. An informed type has valuable expertise for the consumer, whereas an uninformed type does not. The uninformed type cannot mimic the informed type, suggesting that the informed type can build a reputation for competence. However, I find that the relationship breaks down completely if the recommender is sufficiently patient. In Chapter 3, which is co-authored with Florian Ederer, we embed probabilisticlie detection in a standard model of Bayesian persuasion. We show that the Sender lies more when the lie detection probability increases. Moreover, the Sender’s and the Receiver’s equilibrium payoffs are unaffected by a weak lie detection technology because the Sender compensates by lying more. In Chapter 4, I analyze optimal contracting for experimentation when the agent who experiments and the principal who provides incentives agree to disagree over the quality of the project. If efforts are contractible, the principal prefers to reward good outcomes (efforts) exclusively for a more (less) optimistic agent. Moreover, longer experimentation is sustained with non-common prior. If efforts are not contractible, the optimal duration of experimentation is increasing in the agent’s confidence

Information in Games.

In the first chapter, we tightly bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. To do this, we develop a tractable new solution concept for standard repeated games with perfect monitoring: Markov Perfect Correlated Equilibrium generalizes the operator approach of Abreu, Pearce and Stacchetti (1990), but instead takes correlated equilibrium of the auxiliary game. We show that for any private monitoring structure, the set of sequential equilibrium payoffs of a repeated game is contained within the set of Markov Perfect Correlated Equilibrium payoffs. The second chapter extends the Blackwell comparison of experiments to a strategic setting. We introduce a new partial order more strategically informative --- information held by players is "better'' --- and prove it is equivalent to the partial order more strategically valuable --- the ability to induce more equilibrium payoff vectors in all Bayesian games. The centerpiece application is to repeated games with private monitoring where the more strategically informative order ranks monitoring structures. Consequently, we can show when a change in monitoring structure will weakly expand the set of sequential equilibria. The third chapter deals with the tragedy of the commons. When effort imposes negative externalities, competition results in excessive aggregate effort. One way to curb these excesses is for subsets of competitors to form groups which share output or gross revenue. In theory, if the right number of groups forms, Nash equilibrium aggregate effort should fall to the socially optimal level. We investigate experimentally whether individuals manage to form the efficient number of groups and to invest within the chosen groups as theory predicts. Although we observe some systematic departures from theory, we find that subjects vote in most cases to divide themselves into the optimal number of output-sharing groups and, when investing within such groups, curtail inefficiency by 50% to 71%.Ph.D.EconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86380/1/jscherry_1.pd

A Theory of Self-Enforcing Indefinite Agreements

One of the core principles of contract law is the requirement of definiteness. Conventional wisdom holds, however, that the indefiniteness doctrine is largely ignored by courts. In this Article, Professor Scott examines the contemporary case law on indefinite contracts and his review yields three striking findings. First, there is a surprisingly high volume of litigation. Second, the indefiniteness doctrine lives on in the common law of contracts. Third, a large number of the indefiniteness cases involve contracts that are "deliberately" incomplete-that is, parties have declined to condition performance on available, verifiable measures that could be specified in the contract at relatively low cost. These findings raise a fundamental question: Why do parties write deliberately incomplete agreements in the shadow of a robust indefiniteness doctrine? One answer is that these agreements may be self-enforcing. But most of the recently litigated cases involve contracts that do not appear to be self-enforcing in the traditional sense. A second answer is indicated by recent work in experimental economics, which suggests that roughly half the population behave as if reciprocity were an important motivation, while the other half react as if motivated entirely by self-interest. This evidence of a taste for "reciprocal fairness" in nearly half the population, argues Professor Scott, may expand the domain of self-enforcing contracts beyond what is conventionally understood. It may also support a theory that predicts that deliberately incomplete contracts that rely on self-enforcement through reciprocal fairness between strangers are more efficient than the alternative of more complete, legally enforceable agreements

Trust and adaptive rationality : towards a new paradigm in trust research

Combining economic, social-psychological and sociological approaches trust, this book provides a general theoretical framework to explain conditional and unconditional trust; it also presents an experimental test of the corresponding integrative model and its predictions. Broadly, it aims at advancing a ‘cognitive turn’ in trust research by highlighting the importance of (1) an actor´s context-dependent definition of the situation and (2) the flexible and dynamic degree of rationality involved in the phenomenon. In essence, trust is as “multi-faceted” as there are cognitive routes that take us to the choice of a trusting act. Therefore, adaptive rationality has to be incorporated as an independent and orthogonal dimension to the typological space of trust. Going from description to prediction, the work develops an analytically precise and tractable model of trust and adaptive rationality. The empirical test presented combines trust games, high- and low-incentive conditions, framing manipulations, and psychometric measurements; it is complemented by decision-time analyses