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Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values
Theory and Decision ( IF 0.802 ) Pub Date : 2020-11-07 , DOI: 10.1007/s11238-020-09781-1
Koji Yokote , Takumi Kongo , Yukihiko Funaki

In cooperative game theory with transferable utilities (TU games), there are two well-established ways of redistributing Shapley value payoffs: using egalitarian Shapley values, and using consensus values. We present parallel characterizations of these classes of solutions. Together with the (weaker) axioms that characterize the original Shapley value, those that specify the redistribution methods characterize the two classes of values. For the class of egalitarian Shapley values, we focus on redistributions in one-person unanimity games from two perspectives: allowing the worth of coalitions to vary, while keeping the player set fixed; and allowing the player set to change, while keeping the worth of coalitions fixed. This class of values is characterized by efficiency, the balanced contributions property for equal contributors, weak covariance, a proportionately decreasing redistribution in one-person unanimity games, desirability, and null players in unanimity games. For the class of consensus values, we concentrate on redistributions in \((n-1)\)-person unanimity games from the same two perspectives. This class of values is characterized by efficiency, the balanced contributions property for equal contributors to social surplus, complement weak covariance, a proportionately decreasing redistribution in \((n-1)\)-person unanimity games, desirability, and null players in unanimity games.



中文翻译:

重新分配给生产力较低的人:平等主义者沙普利和共识值的并行表征

在具有可转移效用的合作博弈理论(TU游戏)中,有两种行之有效的重新分配Shapley价值收益的方法:使用均等Shapley值和使用共识值。我们提出了这些解决方案类别的并行表征。连同描述原始Shapley值的(较弱)公理一起,指定重新分配方法的公理则描述了这两种值。对于平均主义的Shapley值类别,我们从两个角度着眼于单人一致游戏中的重新分配:允许联盟的价值变化,同时保持玩家固定;并允许玩家进行更改,同时保持联盟的价值不变。此类价值的特征是效率,平等贡献者的平衡贡献属性,弱协方差,一人一致游戏中的重新分配比例,可取性以及一致游戏中的零参与者都成比例减少。对于共识值类别,我们专注于\((n-1)\)-从相同的两个角度来看人人一致的游戏。此类价值的特征是效率,对社会剩余的平等贡献者的平衡贡献属性,对弱协方差的补充,\((n-1)\)人一致博弈中按比例减少的再分配,合意性以及一致中的零参与者游戏。

更新日期:2020-12-23
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