Statistics Papers

Document Type

Journal Article

Date of this Version

10-2003

Publication Source

Games and Economic Behavior

Volume

45

Issue

1

Start Page

73

Last Page

96

DOI

10.1016/S0899-8256(03)00025-3

Abstract

Consider a finite stage game G that is repeated infinitely often. At each time, the players have hypotheses about their opponents' repeated game strategies. They frequently test their hypotheses against the opponents' recent actions. When a hypothesis fails a test, a new one is adopted. Play is almost rational in the sense that, at each point in time, the players' strategies are ϵ-best replies to their beliefs. We show that, at least 1−ϵ of the time t these hypothesis testing strategies constitute an ϵ-equilibrium of the repeated game from t on; in fact the strategies are close to being subgame perfect for long stretches of time. This approach solves the problem of learning to play equilibrium with no prior knowledge (even probabilistic knowledge) of the opponents' strategies or their payoffs.

Copyright/Permission Statement

© 2003. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Keywords

repeated game, Nash equilibrium, subgame perfect equilibrium, hypothesis test

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Date Posted: 27 November 2017

This document has been peer reviewed.