Cooperative Games (von Neumann-Morgenstern Stable Sets)
Cooperative Games (von Neumann-Morgenstern Stable Sets)
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合作博弈（冯·诺依曼-摩根斯坦稳定集）
DOI：
10.1007/978-3-642-27737-5_99-2
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
and Shigeo Muto
中科院分区：
文献类型：
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作者：
Ryo Kawasaki;Jun Wako;and Shigeo Muto
冯·诺依曼-摩根斯坦稳定集（vonNeumann-Morgenstern stable set，以下简称稳定集）是合作对策论中的第一个解概念，由J·冯·诺依曼和O·摩根斯坦提出。摩根斯坦虽然稳定集的定义是针对合作博弈的特征函数形式，但冯·诺依曼和摩根斯坦给出了抽象博弈中更一般的稳定集定义。后来，格林伯格和M。Chwe为将稳定集的概念应用于战略和广泛形式的非合作博弈分析开辟了一条道路。特征函数形式博弈中的稳定集可能不存在，正如WF Lucas对不允许稳定集的十人博弈所证明的那样。另一方面，稳定集存在于许多重要的博弈中。例如，在投票博弈中，稳定集是存在的，它们详细地指出了可以形成什么样的联盟。另一方面，核心在投票博弈中可以是空的，尽管它是合作博弈论中最著名的解决方案概念之一。稳定集的分析不一定是简单的，因为它可以揭示各种可能性。然而，稳定集让我们深入了解参与者的行为，如联盟的形成，在经济，政治和社会情况。
The von Neumann-Morgenstern stable set (hereafter stable set) is the first solution concept in cooperative game theory defined by J. von Neumann and O. Morgenstern. Though it was defined for cooperative games in characteristic function form, von Neumann and Morgenstern gave a more general definition of a stable set in abstract games. Later, J. Greenberg and M. Chwe cleared a way to apply the stable set concept to the analysis of noncooperative games in strategic and extensive forms. Stable sets in a characteristic function form game may not exist, as was shown by WF Lucas for a ten-person game that does not admit a stable set. On the other hand, stable sets exist in many important games. In voting games, for example, stable sets exist, and they indicate what coalitions can be formed in detail. The core, on the other hand, can be empty in voting games, though it is one of the best-known solution concepts in cooperative game theory. The analysis of stable sets is not necessarily straightforward, since it can reveal a variety of possibilities. However, stable sets give us deep insights into players’ behavior, such as coalition formation, in economic, political, and social situations.