Social penalty promotes cooperation in a cooperative society

Why cooperation is well developed in human society is an unsolved question in biological and human sciences. Vast studies in game theory have revealed that in non-cooperative games selfish behavior generally dominates over cooperation and cooperation can be evolved only under very limited conditions. These studies ask the origin of cooperation; whether cooperation can evolve in a group of selfish individuals. In this paper, instead of asking the origin of cooperation, we consider the enhancement of cooperation in a small already cooperative society. We ask whether cooperative behavior is further promoted in a small cooperative society in which social penalty is devised. We analyze hawk-dove game and prisoner's dilemma introducing social penalty. We then expand it for non-cooperative games in general. The results indicate that cooperation is universally favored if penalty is further imposed. We discuss the current result in terms of the moral, laws, rules and regulations in a society, e.g., criminology and traffic violation.