Robust social norms in bargains and markets

We consider the social norms of repeated matching games in the presence of finite probability trembles and show that such norms must be subgame perfect along the equilibrium path but need not be subgame perfect off the equilibrium path. This is consistent with the well known experimental results by Roth et. al. (1991) in which subjects play subgame perfect equilibria in the market game but play non-subgame perfect equilibria in the ultimatum game, providing a simple and intuitive explanation for this behavior in terms of societal norms, where societal norms are simply the dominant play induced by the sequential equilibria arising in societal games. Our analysis provides a fully rational explanation of behavior that has been typically analyzed as arising from boundedly rational play. It also emphasizes the importance of studying the effects of finite tremble probabilities and population sizes directly, for example both limits, very large, and very small populations yield misleading predictions for the intermediate case.