Correlated Equilibrium, Conformity, and Stereotyping in Social Groups


  • We are grateful to participants for comments at presentations of this work at the European Meetings of the Economic Society, 2007; Hebrew University Center for Rationality, 2006; Stony Brook Game Theory International Conference, 2006; SING (Spanish, Italian, Netherlands Game Theory) Meeting (plenary lecture), 2006; Society for Economic Design Conference, 2004; Northwestern University Kellogg Centre for Game Theory, 2004; and at a number of other universities where this paper was presented. We thank Rod Garett and John Wu for reading the paper.


We argue that a social norm and the coordination of behavior within social groups can be expressed by a correlated equilibrium. Given a social group structure (a partition of individuals into social groups), we propose four conditions that one may expect of a correlated equilibrium consistent with social norms. These are: (1) within-group anonymity (conformity within groups), (2) group independence (no conformity between groups), (3) homophily (individuals in the same group have similar attributes), and (4) predictable group behavior (ex post stability). We demonstrate that correlated equilibrium satisfying (1)–(3) exist very generally and equilibrium satisfying (1)–(4) exist in games with many players. We also consider stereotyped beliefs—beliefs that all individuals in a social group can be expected to behave in the same way—and show that stereotyping is not costly to the person who stereotypes but may or may not be beneficial to society.