Essays on Self-Referential Games

This dissertation studies self-referential games in which agents can learn (perfectly and imperfectly) about an opponents\u27 intentions from a private signal. In the first chapter, my main focus is on the interaction of two sources of information about opponents\u27 play: direct observation of an opponent\u27s code of conduct and indirect observation of the same opponent\u27s play in a repeated setting. Using both sources of information I prove a folk theorem for repeated self-referential games with private monitoring. In the second chapter, I investigate the impact of self-referentiality on bad reputation games in which the long-run player must choose specific actions to make short-run players participate in the game. Since these particular actions could be interpreted as evidence of perverse behavior, the long-run agent attempts to separate himself from other types and this results in efficiency losses. When players identify intentions perfectly, I show that inefficiencies and reputational concerns due to a bad reputation disappear. In the case of imperfect observation, I find that self-referentiality and stochastic renewal of the long-run player together overcome inefficiencies because of bad reputation. In the third chapter, I address the timing of signals in self-referential games. These models typically suppose that intentions are divined in a pre-play phase; however, in many applications this may not be the case. For games with perfect information when players observe signals in advance, I show that any subgame perfect equilibria of an infinite-horizon game coincides with a Nash equilibrium of the self-referential finite-horizon approximation of the original game. Then, I focus on two specific classes of games. First, in finitely repeated games with discounting I show that a version of the folk theorem holds regardless of the time at which signals are observed. Second, I examine exit games in which players can terminate the game at any stage. In contrast to repeated games, I find that the equilibrium outcome of the self-referential exit game is unique if signals arrive after the first stage, whereas a folk theorem results only if they occur before the first stage. Finally, I explore asynchronous monitoring of intentions where players may not receive signals simultaneously. With asynchronicity, a folk theorem continues to apply for repeated games; however, for exit games there is a unique equilibrium outcome independent of signal timing, or indeed, independent of having a signal

Collective reputation, social norms, and participation:

This paper analyzes a repeated games model of collective reputation with imperfect public monitoring and perfect local peer monitoring of efforts. Even when peer monitoring is local, firms may achieve higher profits under collective reputation by decreasing the cost of maintaining customers' trust. The optimal number of firms that share a common reputation is greater when (1) trades are more frequent and public information is disseminated more rapidly, (2) the deviation gain is smaller compared to the quality premium, (3) customers' information regarding firms' quality is more precise, or (4) intragroup information about firms' quality is more global. From a positive perspective, we suggest how social norms can influence the reputation of regional products. We also offer an efficiency explanation for food scares. From a normative point of view, in our model, protection of geographical indications increases and mandatory traceability decreases welfare and incentives to provide quality without taking into account direct implementation costs.collective reputation, free riding, public monitoring, peer monitoring, peer sanction,

Disappearing Private Reputations in Long-Run 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 short-lived 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 long-lived 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 finitely-repeated games.Reputation, Imperfect Monitoring, Repeated Games, Commitment, Private Beliefs

Disappearing Private Reputations in Long-Run 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 short-lived 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 long-lived and has private beliefs, so that the informed player’s reputation is private.Reputation, Imperfect Monitoring, Repeated Games, Commitment, Private Beliefs

Sustainable Reputations with Rating Systems

In a product choice game played between a long lived seller and an infnite sequence of buyers, we assume that buyers cannot observe past signals. To facilitate the analysis of applications such as online auctions (e.g. eBay), online shopping search engines (e.g. BizRate.com) and consumer reports, we assume that a central mechanism observes all past signals, and makes public announcements every period. The set of announcements and the mapping from observed signals to the set of announcements is called a rating system. We show that, absent reputation effects, information censoring cannot improve attainable payoffs. However, if there is an initial probability that the seller is a commitment type that plays a particular strategy every period, then there exists a finite rating system and an equilibrium of the resulting game such that, the expected present discounted payoff of the seller is almost his Stackelberg payoff after every history. This is in contrast to Cripps, Mailath and Samuelson (2004), where it is shown that reputation effects do not last forever in such games if buyers can observe all past signals. We also construct .nite rating systems that increase payoffs of almost all buyers, while decreasing the seller’s payoff.Reputations, Rating Systems, Online Reputation Mechanisms, Disappearing Reputations, Permanent Reputations. JEL Classification Numbers: D82