The Conditions for Sustaining Efficient and Inefficient Norms

Although most rational choice theorists have assumed that social norms are created to prevent negative externalities, some norms spoil the welfare of people. These inefficient norms have been discussed as “unpopular norms,” which typically include “the emperor’s new clothes,” self-destructive adolescent behavior, infibulation, and honor killing. However, it is also true that efficient norms, which prevent uncooperative behavior, are observed in social dilemma situations. In this paper, we hypothesize that long-term relations stabilize both efficient and inefficient norms, but communications destabilize inefficient norms. We analyze a Sub-game Perfect Nash Equilibrium (SPNE) and a Strong Perfect Equilibrium (SPE) in an N-person repeated prisoners’ dilemma with the costly punishment option. A social norm is defined as an equilibrium in which every player is expected to do something (or refrain from doing something) and is punished by some or all other members if s/he deviates from this expectation. Two equilibrium concepts reflect a player’s ability to communicate. A strategy profile is an SPNE if no player can carry out solitary deviations (change his/her strategy). This equilibrium concept assumes a situation such that players cannot communicate with each other, e.g. tacit price collusions in oligopoly markets. As the Folk theorem indicates, there exist inefficient SPNEa, in which the Pareto-deficient payoff is sustained by costly punishment. In contrast, an SPE assumes a situation such that self-interested players can engage in cheap talk and collude. If feasible coalitional deviation exists, all members of the coalition can earn more by changing their strategies simultaneously. Every SPE is an SPNE, but the opposite is not true. The sufficient condition for existing SPEa is proved using the multi-objective dynamic programming method. In conclusion, we successfully formalize the hypothesized relationship between efficiency of norms, long-term relations, and communications among players. Additionally, we point out some notable implications.