Behavioral Properties of Correlated Equilibrium; Social Group Structures with Conformity and Stereotyping

We explore the potential for correlated equilibrium to capture conformity to norms and the coordination of behavior within social groups. Given a partition of players into social groups we propose properties that one may expect of a correlated equilibrium: within-group anonymity, group independence, predictable group behavior and stereotyped beliefs. We then demonstrate that (a) a correlated equilibrium satisfying these properties exists in games with many players (b) a player who stereotypes other players cannot do better with correct beliefs and (c) correlation allows predictability of group behavior, which ensures that a correlated equilibrium is approximately ex-post stable.