Potentials and solutions of cooperative games with a fixed player set
Potentials and solutions of cooperative games with a fixed player set
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固定玩家集合作博弈的潜力与解决方案
DOI：
10.1007/s00182-023-00839-2
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发表时间：
2023
影响因子：
0.6
通讯作者：
Nakada Satoshi
中科院分区：
文献类型：
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作者：
Abe Takaaki;Nakada Satoshi
本文考虑了具有固定玩家集且承认潜在函数的合作博弈的解决方案。如果根据势函数将解作为边际贡献给出，则我们说解承认势函数。 Hart 和 Mas-Colell (Econometrica 57(3):589–614, 1989) 表明，Shapley 值是唯一有效的解决方案，并且承认具有可变玩家集的博弈的 HM 势函数。首先，我们认为，如果我们消除效率，各种解决方案都会承认潜在的功能。其次，我们为具有固定玩家集的游戏定义潜在函数，并通过提供通用函数形式来表征承认潜在函数的解决方案的类别。最后，我们将势函数与 Shapley 值遵循的公理相关联，这揭示了为什么效率要求唯一地确定了该类解决方案中的 Shapley 值。
This paper considers the solutions of cooperative games with a fixed player set that admit a potential function. We say that a solution admits a potential function if the solution is given as the marginal contribution according to the potential function. Hart and Mas-Colell (Econometrica 57(3):589–614, 1989) show that the Shapley value is the only solution that is efficient and admits the HM potential function for games with variable player sets. First, we argue that various solutions admit a potential function if we remove efficiency. Second, we define a potential function for games with a fixed player set and characterize the class of the solutions that admit a potential function by providing their general functional form. Finally, we associate a potential function with the axioms that the Shapley value obeys, which uncovers why the efficiency requirement uniquely pins down the Shapley value in the class of solutions.