正则对策的N-M稳定集及其唯一存在定理  

N-M STABLE SET OF A REGULAR GAME AND ITS UNIQUE EXISTENCE THEOREM

作　　者：姜殿玉[1] 

机构地区：[1]淮海工学院对策论及其应用研究所,连云港222005

出　　处：《系统科学与数学》2010年第7期958-962,共5页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(70871051)资助课题

摘　　要：研究了有非对称性和负传递性偏好的无限策略对策,提出了N-M稳定集和正则对策的概念,其中N-M稳定集是将合作对策中由Von Neumann和Morgenstern给出的相应概念引入到策略对策中的.所谓正则对策是指其Nash均衡集中每条链关于一致偏好总有上界的无限策略对策.证明了每个正则对策都有唯一N-M稳定集.此结果及其应用例子说明正则对策N-M稳定集的概念对于策略对策的纯Nash均衡的精炼起着重要作用.This paper is concerned with infinite strategic games with asymmetric and negatively transitive preferences.An N-M stable set in a strategic game is introduced by the analogous way given by von Neumann and Morgenstern in cooperative games.An infinite strategic game is regular if every chain in the set of Nash equilibria with respect to the uniform preference is upper bounded.It is shown that every regular game has a unique N-M stable set. The result and its applied example show that the concept of N-M stable set in regular games plays an important role to refine pure Nash equilibria.

关 键 词：正则对策 N-M稳定集 流浪汉对策 偏好 ZORN引理 

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