Institute for Mathematical Behavioral Sciences

Standard economic models assume that if we take a group of players, say i, j and k, interacting repeatedly with each other, then i's strategy towards j depends on what happens between i and j and does not depend on what happens between j and k or i and k. This assumes away the existence of third party sanctions, imitation of third party behaviors and other "social institutions." Similarly, i's utility is typically assumed to be only a function of his interactions with j and k. This assumes away considerations of envy, fairness, equality, etc.

But, can we justify such assumptions on theoretical grounds? If a game were to allow for the existence of social institutions (e.g., is strategy towards j is may depend on what happens between j and k) would its equilibria necessitate, or at least allow for, their absence? I prove that the opposite holds. Social institutions are necessary for the existence of a robust equilibrium, in a very general class of games.

More specifically, a theorem is proved showing that there are three types of social institutions that are necessary and sufficient for the existence of a robust equilibrium; they correspond to third party sanctions, conformity and internalized norms.