The development process of social organizations : A game theoretic approach

社会是竞争与合作的混合体。本研究的目的是运用非合作博弈论来考察各种社会组织是如何通过追求个体价值的主体之间的自愿协议来形成和发展的。主要研究结果如下：(1)建立了囚徒困境博弈的动态模型，允许参与者组成一个合作组织。一个组织由四个因素建模：(I)成员集合，(Ii)监督代理的成本，(Iii)对偏离者的惩罚规则，(Iv)分配规则。当存在非成员的机会主义(搭便车)行为时，所有代理的组织并不总是形成，每个参与者都做出参与该组织的概率决定。参与者的参与概率由人口规模、盈利组织的最小规模以及参与收益与不参与收益的激励比决定。对该模型进行了扩展，使其能够通过不重叠的世代来捕捉组织发展。我们的动态分析表明，在人口没有快速增长的情况下，存在一个社会发展的临界水平，超过这个水平就不会形成任何组织。(2)研究了联盟形成和组织内收益分配的讨价还价问题。在随机提出者规则下，证明了均衡状态下不存在协议延迟，也不一定能达到完全合作。我们进一步调查重新谈判的可能性如何提高协议的效率。

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.