Social conformity in games with many players

In the literature of psychology and economics it is frequently observed that individuals tend to imitate similar individuals. A fundamental question is whether the outcome of such imitation can be consistent with self-interested behaviour. We propose that this consistency requires the existence of a Nash equilibrium that induces a partition of the player set into relatively few groups of similar individuals playing the same or similar strategies. In this paper we define and characterise a family of games admitting existence of approximated Nash equilibria in pure strategies that induce partition of the player sets with the desired properties. We also introduce the Conley-Wooders concept of 'crowding types' into our description players and distinguish between the crowding type of a player - those characteristics of a player that have direct effects on others - and his tastes, taken to directly affect only that player. With this assumption of 'within crowding type anonymity' and a 'convexity of taste-types' assumption we show that the number of groups can be uniformly bounded.