A Game Theoretical Analysis on Linkage between Groups Relation and Individuals Relation

Although Georg Simmel emphasized the three layers of society that are individual, organization, and society, there are few socio-mathematical or rational-choice models assuming the three layers in the previous research. Then I build up such a model using the game theory and social dilemma theory, aiming to explicate the complicated linkage between inter-groups interaction and inter-individuals interaction. Assume that the society in this model is composed of two groups named A, B that may be nations, companies, communities, organizations and so on. Assume that each group is composed of many individuals as members who play a kind of an N-person chicken game similar to social dilemma. Assume that the individuals rationally choose their action (Cooperate or Defect), whereas the Groups have no choice. The action of group A member influences not only the same group (A) members but also the other group (B) members through the cooperation rate of the group A. Assuming the groups to be nations, the cooperation rate of the nation may mean military power. High cooperation rate of nation A may let down the nation B members' payoffs through the war between nation A and B. Cooperation may be not only good for self-group but also bad for other-group. The ambivalent nature of cooperation will be very familiar to us in our daily life but it has almost not been modeled. From above assumptions I show what happens in this model society.