Correlated equilibrium and behavioral conformity∗

Is conformity amongst similar individuals consistent with self-interested behavior? We consider a model of incomplete information in which each player receives a signal, interpreted as an allocation to a role, and can make his action choice conditional on his role. Our main result demonstrates that ‘near to’ any correlated equilibrium is an approximate correlated equilibrium ‘with conformity’ — that is, an equilibrium where all ‘similar players’ play the same strategy, have the same probability of being allocated to each role, and receive approximately the same payoff; in short, similar players ‘behave in an identical way’ and are treated nearly equally. To measure ‘similarity’ amongst players we introduce the notions of approximate substitutes and a (δ,Q)-class games — a game with Q classes of players where all players in the same class are δ-substitutes for each other. ∗This paper is a major revision of Cartwright and Wooders (2003a). The main results of that paper were presented at the the 2002 General Equilibrium Conference held in Athens in May 2002 and at Northwestern University in August 2002. We thank the participants for their interest and comments.