The development process of social organizations : A game theoretic approach

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Society is an intermixture of competition and cooperation. The purpose of this research is to investigate by noncooperative game theory how various kinds of social organizations form and develop through voluntary agreements among agents pursuing individual values. The main results are summarized below.(1) We present a dynamic model of the prisoner's dilemma game in which playrs are allowed to form an organization for cooperation. An organization is modeled by four factors : (i) the set of members, (ii) costs for monitoring agents, (iii) punishment rule for deviators, (iv) distribution rule. When the opportunistic (free-riding) behavior by non-members exists, the organization of all agents does not always form and each playr makes a probabilistic decision to participate in the organization. The participation probability for a playr is determined by the population size, the minimum size for a profitable organization, and incentive ratio of the profit of participation to that of non-participation. The model is extended so that it can capture the organizational development by non-overlapping generations. Our dynamic analysis shows that there exists a critical level of social development beyond which no organization forms, given that the population does not grow rapidly.(2) The bargaining problem of coalition formation and of payoff distribution within an organization is investigated. Under the random proposer rule, it is proved that no delay of agreements exists in equilibrium and that the full cooperation is not always attained. We further investigate how the possibility of renegotiation can enhance the efficiency of the agreement.