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

Self-Commitment-Institutions and Cooperation in Overlapping Generations Games

This paper focuses on a two-period OLG economy with public imperfect observability over the intergenerational cooperative dimension. Individual endowment is at free disposal and perfectly observable. In this environment we study how a new mechanism, we call Self-Commitment-Institution (SCI), outperforms personal and community enforcement in achieving higher ex-ante e¢ ciency. Social norms with and without SCI are characterized. If social norms with SCI are implemented, agents might freely dispose of their endowment. As long as they reduce their marginal gain from deviation in terms of current utility, they also credibly self-commit on intergenerational cooperation. Under quite general conditions we .nd that, even if individual strategies are still characterized by behavioral uncertainty, the introduction of SCI relaxes the inclination toward opportunistic behavior and sustains higher e¢ ciency compared to social norms without SCI. We quantify the value of SCI and investigate the role of memory with di¤erent social norms. Finally, applications on intergenerational public good games and transfer games with productive SCI are providedCooperation; Free disposal; Imperfect public monitoring; Memory; Overlapping generation game; Self-Commitment Institution;

Self-Commitment-Institutions and Cooperation in Overlapping Generations Games

This paper focuses on a two-period OLG economy with public imperfect observability over the intergenerational cooperative dimension. Individual endowment is at free disposal and perfectly observable. In this environment we study how a new mechanism, we call Self-Commitment-Institution (SCI), outperforms personal and community enforcement in achieving higher ex-ante efficiency. Social norms with and without SCI are characterized. If social norms with SCI are implemented, agents might freely dispose of their endowment. As long as they reduce their marginal gain from deviation in terms of current utility, they also credibly self-commit on intergenerational cooperation. Under quite general conditions we find that, even if individual strategies are still characterized by behavioral uncertainty, the introduction of SCI relaxes the inclination toward opportunistic behavior and sustains higher efficiency compared to social norms without SCI. We quantify the value of SCI and investigate the role of memory with different social norms. Finally, applications on intergenerational public good games and transfer games with productive SCI are provided.Cooperation, Free disposal, Imperfect public monitoring, Memory, Overlapping generation game, Self-Commitment Institution

The role of information in repeated games with frequent actions

We show that the ways incentives can be provided during dynamic interaction depend very crucially on the manner in which players learn information. This conclusion is established in a general stationary environment with noisy public monitoring and frequent actions. The monitoring process can be represented by a sum of a multi-dimensional Brownian component and a jump process. We show that jumps can be used to provide incentives both with transfers and value burning while continuous information can be used to provide incentives only with transfers. Also, it is asymptotically optimal to use the cumulative realization of the Brownian component linearly. Additionally, we approximate the equilibrium payoff set for fixed small discount rates as the periods become short by a series of linear programming problems. These problems highlight how the two types of information can be used to provide incentives.repeated games, dynamic incentives, frequent moves

An anti-folk theorem for finite past equilibria in repeated games with private monitoring

We prove an anti-folk theorem for repeated games with private monitoring. We assume that the strategies have a finite past (they are measurable with respect to finite partitions of past histories), that each period players' preferences over actions are modified by smooth idiosyncratic shocks, and that the monitoring is sufficiently connected. In all repeated game equilibria, each period play is an equilibrium of the stage game. When the monitoring is approximately connected, and equilibrium strategies have a uniformly bounded past, then each period play is an approximate equilibrium of the stage game.Repeated games, anti-folk theorem, private monitoring

Recursive Methods in Discounted Stochastic Games: An Algorithm for delta Approaching 1 and a Folk Theorem

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period’s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.Stochastic games

Communication in Dynastic Repeated Games: `Whitewashes' and `Coverups

We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication. When communication is costless and messages are sent simultaneously, communication mechanisms or protocols exist that sustain the same set of equilibrium payoffs as in the standard repeated game. When communication is costless but sequential, the incentives to `whitewash' the unobservable past history of play become pervasive. These incentives to whitewash can only be countered if some player serves as a `neutral historian' who verifies the truthfulness of others' reports while remaining indifferent in the process. By contrast, when communication is sequential and (lexicographically) costly, all protocols admit only equilibria that sustain stage Nash equilibrium payoffs. We also analyze a centralized communication protocol in which history leaves a `footprint' that can only hidden by the current cohort by a unanimous `coverup'. We show that in this case only weakly renegotiation proof payoffs are sustainable in equilibrium.Dynastic Repeated Games, Communication, Whitewashing, Coverups

Delayed-response strategies in repeated games with observation lags

We extend the folk theorem of repeated games to two settings in which players' information about others' play arrives with stochastic lags. In our first model, signals are almost-perfect if and when they do arrive, that is, each player either observes an almost-perfect signal of period-t play with some lag or else never sees a signal of period-t play. The second model has the same lag structure, but the information structure corresponds to a lagged form of imperfect public monitoring, and players are allowed to communicate via cheap-talk messages at the end of each period. In each case, we construct equilibria in “delayed-response strategies,” which ensure that players wait long enough to respond to signals that with high probability all relevant signals are received before players respond. To do so, we extend past work on private monitoring to obtain folk theorems despite the small residual amount of private information.EconomicsEngineering and Applied Science