Behavioral conformity in games with many players

In the literature of psychology and economics it is frequently observed that individuals tend to conform in their behavior to that of similar individuals. A fundamental question is whether the outcome of such conformity can be consistent with self-interest. We propose that this consistency requires the existence of a Nash or approximate Nash equilibrium that induces a partition of the player set into relatively few societies, each consisting of similar individuals playing similar strategies. In this paper we characterize a family of games admitting the existence of such equilibrium. We also introduce the concept of 'crowding types' into our description of players and distinguish between the crowding type of a player-those characteristics of a player that have direct effects on others-and his tastes. With assumptions of 'within crowding type anonymity' and 'linearity of taste-types' we show that the number of societies can be uniformly bounded.