缺原子博弈理论与应用综述

A Survey of Non-atomic Game Theory and Its Application

2005年,诺贝尔经济学奖获得者奥曼和博弈论专家夏普利在20世纪60年代开创了缺原子博弈问题的研究,目前缺原子博弈理论已经发展成为博弈论重要的分支之一。本文主要从缺原子博弈模型、缺原子博弈的类似值的概念和类似解的概念、具有模糊联盟的缺原子博弈几个方面,对缺原子博弈理论进行了总结,并简单介绍了缺原子博弈的应用现状,对缺原子博弈可能的发展趋势进行预测。本文力图通过对相关文献的总结,以促进国内对缺原子博弈的研究工作。

Non-atomic game theory has been the one of important branch of game theory, which was founded by R. J. Aumann who won the Nobel economic prize in 2005 and L. S. Shapley in the early 1960s. In this paper we summarized the framework of non-atomic game theory from the model of non-atomic games, value-like concepts and .solution-like concepts of non-atomic games and non-atomic games with fuzzy coalition; we simply introduced the applications of the non- atomic game theory and predicted the possible forecast of it. Since domestic researches on non-atomic games were little done, this paper can motivate the domestic researches on non-atomic games.