Cooperation and bounded recall

Robert J. Aumann and Sylvain Sorin

Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel
Département de Mathématiques, University Louis Pasteur, 67084, Strasbourg, France

Available online 27 July 2004.

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).