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.