Conformity, Equity and Correlated Equilibrium

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 three proper-ties one may expect of a correlated equilibrium: within-group anonymity, group independence and stereotyped beliefs. Within-group anonymity requires that players within the same social group have equal opportunities and equal payoffs. Group independence requires that there be no correlation of behavior between groups. If beliefs are stereotyped then any two members of a social group are expected to behave identically. We demonstrate that there are subjective correlated equilibrium satisfying within-group anonymity, group independence and stereotyping. These results apply when players within social groups are ‘similar’, and not necessarily identical. A number of related issues, such as fairness, are also discussed.