Social Conformity in Games with Many Players
34 Pages Posted: 22 Jan 2004
Date Written: December 2003
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.
Suggested Citation: Suggested Citation