Interdependent Relationships in Game Theory: A Generalized Model

A generalized model of games is proposed, with which both cooperative games and non-cooperative games can be expressed and analyzed, as well as those games that are neither cooperative nor non-cooperative. The model is based on relationships between players and supposed relationships. A relationship is a numerical value that denotes how one player cares for the payoffs of another player. A supposed relationship is a player’s belief about the relationship between two players. The players choose their strategies by taking into consideration not only the material payoffs but also relationships and their change. Two games, a prisoner’s dilemma and a repeated ultimatum game, are analyzed as examples of application of this model.