匹配对策模型的核心稳定性  

Core Stability of Matching Games

作　　者：孔亮[1] 方奇志[1] 

机构地区：[1]中国海洋大学数学系,山东青岛266071

出　　处：《运筹与管理》2006年第4期73-78,共6页Operations Research and Management Science

基　　金：国家自然科学基金项目(1037111470571040/G0105)

摘　　要：本文研究匹配合作对策模型的核心稳定性。基于线性规划对偶理论和图论的相关知识,我们首先证明了匹配对策有稳定核心当且仅当其基础二部图有完美匹配。其次我们讨论了几个与核心稳定性密切相关的性质(核心的包容性、对策的精确性和可扩性)并证明了它们的等价性。基于这些结果,我们还讨论了相应问题的算法。In this paper, we study the problem of core stability for matching games. Based on duality theory of linear programming and graph theory, it is proved that the matching game defined on a bipartite graph has the stable core if and only if the graph has a perfect matching. We also show that the properties of core largeness, the extendibility and the exactness for these matching games are equivalent, which strictly imply the stability of the core.

关 键 词：对策论 核心稳定性 对偶定理 匹配合作对策 

分 类 号：O225[理学—运筹学与控制论] O157.6[理学—数学]