Robert J. Aumann and Sylvain Sorin

Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel

DÃ©partement de MathÃ©matiques, University Louis Pasteur, 67084, Strasbourg,
France

Available online 27 July 2004.

Abstract

A two-person game has common interests if there is a single payoff pair z that
strongly Pareto dominates all other payoff pairs. Suppose such a game is repeated
many times, and that each player attaches a small but positive probability
to the other playing some fixed strategy with bounded recall, rather than playing
to maximize his payoff. Then the resulting supergame has an equilibrium in
pure strategies, and the payoffs to all such equilibria are close to optimal
(i.e., to z).