Essays on Repeated Games

Author:

Maenner, Eliot

Graduate Program:

Economics

Degree:

Doctor of Philosophy

Document Type:

Dissertation

Date of Defense:

August 28, 2002

Committee Members:

Vijay Krishna, Committee Chair/Co-Chair
Kalyan Chatterjee, Committee Chair/Co-Chair
Anthony Mark Kwasnica, Committee Member
Tomas Sjostrom, Committee Member
James Schuyler Jordan, Committee Member

Keywords:

learning
bargaining
repeated games
equilibrium selection

Abstract:

The problem of equilibrium selection in repeated games is approached by incorporating explicit models of players’ decision processes into the repeated game. The first essay, “Learning to be Simple: Adaptation and Complexity in the Repeated Prisoners’ Dilemma,” incorporates boundedly rational players into a repeated game who adapt their strategies based on certain simple models they build of each other’s strategies. In the learning process I analyze strategies are represented by finite-state automata and players have a preference for a simpler strategy to a more complex one, provided the two strategies yield the same utility payoff(that is, preferences are lexicographic). The process consists of an inference part, where a player constructs a minimally complex model of the other player based on the observed path of play, and an adaptation part, where a player chooses a best response to one of the inferences. I show, in the context of the infinitely repeated Prisoners’ Dilemma, that the nature of the inference crucially a ffects the nature of the steady states of the dynamical system associated with the inference-adaptation process; an optimistic inference leads players to the unique subgame perfect equilibrium in stationary strategies while a cautious inference leads players to the subset of self-confirming equilibria with Nash outcome paths. The second essay, “Negotiation in Repeated Games,” incorporates an explicit noncooper-ative model of bargaining into a repeated game which is the process by which players switch between continuation payoffs. Players negotiate with each other through an alternating offers protocol while the repeated game is being played to attempt to determine future play. In each stage there are three substages in which the players play the stage game, a continuation payoffs is potentially offered, and the offer is accepted or rejected. I show that when the discount factor is suffciently near one that negotiation-compatible equilibria exist and all negotiation-compatible equilibria in the model are nearly efficient — the players will play a repeated game strategy that is efficient after the first stage.