Population monotonic path schemes for simple games
Population monotonic path schemes for simple games
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简单博弈的群体单调路径方案
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
H. Hamers
中科院分区：
文献类型：
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作者：
B. Çiftçi;P. Borm;H. Hamers
游戏的路径方案由路径组成，即，在联盟形成过程中形成的联盟序列和方案，即，路径中每个联盟的收益向量。如果参与者的收益不随路径联盟的增长而减少，则路径方案称为种群单调。在这项研究中，我们专注于Shapley路径计划的简单游戏中，每个路径联盟的Shapley值的相关子游戏提供了手头的分配。显然，一个博弈的每个Shapley路径方案是种群单调的当且仅当该博弈的Shapley分配方案是Sprumont意义下的种群单调的（Games Econ Behav 2：378-394，1990）。我们证明了一个简单的游戏允许人口单调Shapley路径计划，当且仅当游戏是平衡的。此外，Shapley路径方案是人口单调的当且仅当沿着路径形成的第一个获胜联盟包含每个最小获胜联盟。我们还证明了一个简单的游戏，每个Shapley路径计划是人口单调的当且仅当该游戏的否决者的集合是一个获胜的联盟。扩展这些结果，以其他有效的概率值进行了讨论。
A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed.