具有外部性的合作博弈问题中的稳定的联盟结构

传统的合作博弈问题中,联盟的收益只受到联盟中参与者行为的影响,与其他参与者形成的联盟无关.而在具有外部性影响的环境中,联盟的收益不仅与联盟中参与者行为有关,而且还受到其他参与者形成联盟的影响.本文研究具有外部性的合作博弈问题,分析外部性环境对参与者行为的影响.引入划分函数来描述该合作博弈问题中联盟的收益,提出稳定的联盟结构的概念来描述参与者形成联盟的形式,并说明其存在性.然后通过研究划分函数的性质来说明联盟结构是稳定的充分条件.最后设计演化算法来寻找稳定的联盟结构.本文得到如下结论:对于一个任意的联盟结构,若以它为基础可以把联盟结构集合分为多个部分且每一部分满足一定的性质,则这个联盟结构是稳定的.

Stable coalition structures in cooperative game with externalities

In traditional cooperative game, the worth of a coalition depends only on the coalition. In the environment of externalities, the worth of a coalition not only depends on the coalition itself, but also is affected by other players' coalitions. This paper studies cooperative games with externalities, and analyzes the behaviors of players in these games. We use partition function to describe the worth of coalitions and put forward the definition of stable coalition structures. Then, we illustrate the existence of stable coalition structures. We get the sufficient condition that the coalition structure is stable by analyzing the properties of partition function. Finally, we design an evolutionary algorithm to find these stable coalition structures. We obtain the following conclusions: for a given coalition structure, if the set of all coalition structures can be divided into two separate parts based on this coalition structure, and each part satisfies some properties, this coalition structure is stable.