Essays in the theory of repeated games

Resumen

This thesis comprises three essays in economic theory. The first two are in the theory of repeated games. The third is also a theoretical contribution, which mixes con- cepts both from repeated games and the theory of incentives. The first chapter is a novel contribution to frequent monitoring in repeated games. The second one, studies for the first time, infinitely repeated games where the repetitions of the stage game are random. The last chapter, studies the provision of incentives in a principal-monitor-agent relation with exogenous learning, where the compensation is exogenously fixed. Each chapter can be considered independently of the rest. Chapter I studies frequent monitoring in a simple infinitely repeated game with imperfect public information and discounting, where players observe the state of a continuous time Brownian process at moments in time of length . It shows that a limit folk theorem can be achieved with imperfect public monitoring when players monitor each other at the highest frequency, i.e. ! 0. The approach proposed places distinct initial conditions on the process, which depend on the unknown action profile simultaneously and privately decided by the players at the beginning of each period of the game. The strong decreasing effect on the expected immediate gains from deviation when the interval between actions shrinks, and the associated increase precision of the public signals, make the result possible in the limit. The existence of a positive monotonic relation between payoffs and monitoring intensity is also found. Chapter II studies repeated games where the time repetitions of the stage game are not known or controlled by the players. Many economic situations of interest where players repeatedly interact share this feature; players do not know exactly when the next time they will be called to play the stage game will be. We call this feature random/stochastic monitoring. We show that perfect random monitoring is always better then the classical perfect deterministic monitoring when the players'discount function is convex in the time domain. Surprisingly, when the monitoring is imperfect but public, the result does not extend in the same absolute sense to all frequencies of play. The positive effect in the players'discounting is not always sufficient to compensate for a potential loss in the informational content of the public signals, due to the extra uncertainty on the repetitions of the stage game. However, we establish conditions under which random monitoring allows efficiency gains on the value of the best strongly symmetric equilibrium. Chapter III studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the e¤ort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when re- placement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of benefitting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.-----------------------------------------------------