Mutual support in games: Some properties of Berge equilibria

Olivier Musy,Andrew M Colman,Tom W Körner,Tarik Tazdaït

doi:10.1016/j.jmp.2011.02.001

Abstract

The Berge equilibrium concept formalizes mutual support among players motivated by the altruistic social value orientation in games. We prove some basic results for Berge equilibria and their relations to Nash equilibria, and we provide a straightforward method for finding Berge equilibria in n -player games. We explore some specific examples, and we explain how the Berge equilibrium provides a compelling model of cooperation in social dilemmas. We show that the Berge equilibrium also explains coordination in some common interest games and is partially successful in explaining the payoff dominance phenomenon, and we comment that the theory of team reasoning provides alternative solutions to these problems.

Highlights

This article focuses on the Berge equilibrium concept and explores its relevance to cooperation in social dilemmas and to the related phenomenon of coordination in common interest games
Berge equilibrium can be viewed as an implication of the altruistic social value orientation of interdependence theory, just as Nash equilibrium is an implication of the individualistic orientation
Berge equilibrium provides a compelling model of cooperation in social dilemmas, including the Prisoner’s Dilemma and n-Player Prisoner’s Dilemma games

Summary

Introduction

This article focuses on the Berge equilibrium concept and explores its relevance to cooperation in social dilemmas and to the related phenomenon of coordination in common interest games. In the closely related Centipede game, most players avoid the (subgame-perfect) Nash equilibrium and behave more cooperatively or altruistically, even when very large financial incentives are at stake (Parco, Rapoport, & Stein, 2002); and in the Ultimatum game, players almost always behave more cooperatively or altruistically than is required by the subgame-perfect Nash equilibrium (Camerer & Thaler, 1995) In all such games, intuition and experimental evidence strongly favor strategy choices that deviate systematically from those mandated by motivations that are purely selfish in terms of objective payoffs. The assumption is that players are invariably motivated to maximize their expected utilities, in any situations in which they find themselves, but that that these expected utilities are not necessarily individualistic—they may be altruistic, cooperative, competitive, or equality-seeking, depending on the psychological characteristics of the decision maker and the particular circumstances of the social interaction.

Altruism and the Berge equilibrium

Conclusions