n人合作博弈中k人稳定联盟的存在性

Stable k-person Coalitions in an n-person Cooperative Game

本文在以Nash谈判解为分配准则的前提下,考虑—个n人合作博弈中核心不为空的k人稳定合作联盟的存在性.首先,考察了2人联盟的情形,给出稳定2人联盟的概念并进一步证明在n人合作博弈中必然存在一个稳定2人联盟.接着分析稳定k人联盟,并给出一个稳定k人联盟存在的充分条件.进一步地,设计了一个算法,寻找与存在稳定k人联盟等价的一个匹配.另外,本文还给出了—个K人联盟中所有局中人获得的收益高于其内部子联盟的充分条件.最后给出一个算例,验证本文理论和方法的可行性.

This paper discusses issues of k-person coalitions in the presence of cores in an n-person cooperative game. We take the Nash bargaining solution as our allocation criteria.First, we examine the 2-person coalition and further demonstrate the existence of a stable2-person coalition in an n-person cooperative game. Then, the concept of a stable k-person coalition is proposed and discussion of the existence of a stable k-person coalition follows. In particular,we present a general approach to realize the search of a stable k-person coalition.Moreover, we additionally show a sufficient condition with which all of the players gain more than the subcoalitions in ak-person coalition.Finally, a numerical illustration is given to verify the correctness of the theory put forward in this paper.