Understanding the other through social roles

Inductive game theory has been developed to explore the origin of beliefs of a person from his accumulated experiences of a game situation. It has been restricted to a person's view of the structure not including another person's thoughts. In this paper, we explore the experiential origin of one's view of the other's beliefs about the game situation, especially about the other's payoffs. We restrict our exploration to a 2-role (strategic) game, which has been recurrently played by two people with occasional role-switching. Each person accumulates experiences of both roles, and these experiences become the source for his transpersonal view about the other. Reciprocity in the sense of role-switching is crucial for deriving his own and the other's beliefs. We also consider how a person can use these views for his behavior revision, and we define an equilibrium called an intrapersonal coordination equilibrium. Based on this, we show that cooperation will emerge as the degree of reciprocity increases.