基于匹配序的合作对策联盟形成决策方法及其应用

A Matching Order-Based Coalition Formation Decision-Making Method for Cooperative Games and Its Application

合作对策中,联盟的形成过程是联盟一切活动的基础,直接影响着合作的稳定性与可持续发展。本文在分析局中人心理,情感,现实等因素对联盟形成所产生影响的基础上,首先定义了主观偏好标度值量化了心理、情感等因素,定义了收益分配函数将现实因素量化,构建了综合匹配函数作为局中人选择合作伙伴的一个序标准,通过定义匹配请求、交互匹配、直接交互匹配等概念,构建了基于匹配序的联盟形成决策模型,并证明了在特定情况下直接交互匹配的存在必然性。其次,给出了基于匹配序的联盟形成方法步骤,演化了大联盟的形成过程。最后通过具体实例验证了该决策方法的有效性与合理性。结果表明,该方法能有效的形成一系列可行且稳定的联盟结构,能快速演化联盟的形成过程,为有效解决联盟形成问题奠定了良好基础。

The formation problem of a coalition is the most important part in cooperative games and it will affect the stability and sustainable development of a cooperation process. In this paper, by analyzing various factors affecting the formation of a coalition, firstly we give a set of subjective preference scale values between players in their selection process to quantify some psychological preference factors. Then we provide a profit function between players, so some realistic factors are quantitatively expressed. And furthermore some new concepts such as matching unite, priority matching unite, direct interaction matching are defined, a matching order-based coalition formation decision model is proposed and two important theorems are given to prove that a coalition is formed inevitability under special circumstances. After that some algorithm steps are given. Finally, by a concrete example, the effectiveness of our model is verified. The results show that our model can effectively provide a series of feasible and stable coalition structures and can show the evolution process of the grand coalition quickly. So our model will lay a sound basis for solving some coalition formation problems.