Correlated equilibrium, conformity and stereotyping

We demonstrate that correlated equilibrium can express conformity to norms and the coordination of behavior within social groups. Given a social group structure (a partition of players into social groups), we propose three properties that one may expect of a correlated equilibrium consistent with social group structures satisfying behavioral conformity. These are: (a) within-group anonymity (conformity within groups); (b) group independence (no conformity between groups), and (c) predictable social group behavior (ex-post stability). We also consider stereotyped beliefs --- beliefs that all (other) players in a social group can be expected to behave in the same way. We demonstrate that: (1) Correlated equilibrium satisfying both (a) and (b) exist very generally; (2) If there are many players then a correlated equilibrium satisfying (a), (b) and (c) exists; (3) Stereotyping is not costly to the player who stereotypes.