Equivalence theorem, consistency and axiomatizations of a multi-choice value
Equivalence theorem, consistency and axiomatizations of a multi-choice value
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DOI：
10.1007/s10898-008-9392-9
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发表时间：
2009-12
影响因子：
1.8
通讯作者：
Yan-An Hwang;Y. Liao
中科院分区：
文献类型：
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作者：
Yan-An Hwang;Y. Liao
本文致力于研究多选择博弈的解，该多选择博弈允许一个势，例如与Hsiao和Raghavan提出的扩展Shapley值相关联的势（Int J Game Theory 21：301-302，1992; Games Econ Behav 5：240-256，1993）。几个公理化的家庭的所有解决方案，承认一个潜在的提供，作为一个主要的结果，它表明，这些解决方案中的每一个可以通过应用扩展Shapley值适当修改的游戏。在多选择博弈的框架下，我们还提供了哈特和Mas-Colell（Econometrica 57：589-614，1989）引入的简化博弈的扩展。与Hsiao和Raghavan（1992，1993）的工作不同，我们给出了两种公理化形式，一种是Myerson（Int J Game Theory 9：169-182，1980）基于平衡贡献性质的Shapley值公理化的类似形式。另一个公理化是利用相容性得到的。
This paper is devoted to the study of solutions for multi-choice games which admit a potential, such as the potential associated with the extended Shapley value proposed by Hsiao and Raghavan (Int J Game Theory 21:301–302, 1992; Games Econ Behav 5:240–256, 1993). Several axiomatizations of the family of all solutions that admit a potential are offered and, as a main result, it is shown that each of these solutions can be obtained by applying the extended Shapley value to an appropriately modified game. In the framework of multi-choice games, we also provide an extension of the reduced game introduced by Hart and Mas-Colell (Econometrica 57:589–614, 1989). Different from the works of Hsiao and Raghavan (1992, 1993), we provide two types of axiomatizations, one is the analogue of Myerson’s (Int J Game Theory 9:169–182, 1980) axiomatization of the Shapley value based on the property of balanced contributions. The other axiomatization is obtained by means of the property of consistency.