Interdependent Relationships in Game Theory: A Generalized Model

Abstract: A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships and supposed relationships between players. A relationship is a numerical value that denotes how one player cares for the payoffs of another player, while a supposed relationship is another numerical value that denotes 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 prisoners' dilemma and a repeated ultimatum game, are analyzed as examples of application of this model.