A Mathematical Sociological Analysis toward Clarifying Mechanisms of Social Inequality and Redistribution

本研究的主要成果有以下三点。(1)为了解释社会差距的形成机制，本文构建了两类三人博弈模型，一种是具体的分工和赚钱模型，另一种是一般的三人鸡群博弈模型。阐明了这些博弈均衡的特征。(2)提出了社会效率与平均主义的综合评价原则。具体而言，深入考虑低收益个体的原则是源于两人关系中平等的社会价值取向的自然假设。(3)构建了一个异质行为体同时形成差距和社区的模型。具体而言，建立了一个12人网络博弈模型，并阐明了什么样的差距出现在博弈的均衡网络。

The main results of this research are the following three points. (1) In order to explicating mechanisms of social gap, the two types of three-person game theory model were built; one is concretely a model of division of work and money generation, the other is generally three-person chicken games. The features of the equilibria in these games were clarified. (2) The integrated evaluation principle of social efficiency and egalitarianism was proposed. Specifically, the principle that considers the lower payoff individuals deeply isderived from a natural assumption of the social value orientation toward equality in two-person relation. (3) A model in which the gap and the community were formed simultaneously from heterogeneous actors was built. Specifically, a twelve-person network game model was built, and it was clarified what kind of gap arises as the equilibrium network in the games.