| 匹配对策模型的核心稳定性 |
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| 引用本文： | 孔亮,方奇志.匹配对策模型的核心稳定性[J].运筹与管理,2006,15(4):73-78. |
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| 作者姓名： | 孔亮 方奇志 |
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| 作者单位： | 中国海洋大学,数学系,山东,青岛,266071 |
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| 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。
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| 关 键 词： | 对策论 核心稳定性 对偶定理 匹配合作对策 |
| 文章编号： | 1007-3221(2006)04-0073-06 |
| 收稿时间： | 01 14 2006 12:00AM |
| 修稿时间： | 2006年1月14日 |
Core Stability of Matching Games |
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| KONG Liang,FANG Qi-zhi.Core Stability of Matching Games[J].Operations Research and Management Science,2006,15(4):73-78. |
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| Authors: | KONG Liang FANG Qi-zhi |
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| Institution: | Department of Mathematics, University of China, Qingdao, 266071, China |
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| Abstract: | 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. |
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| Keywords: | game theory core stability duality theorem matching cooperative game |
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