Shapley Mapping and Its Axiomatizations in n-Person Cooperative Interval Games
Shapley Mapping and Its Axiomatizations in n-Person Cooperative Interval Games
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DOI：
10.3390/math10213963
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发表时间：
2022-10
期刊：
影响因子：
2.4
通讯作者：
Junnosuke Shino;S. Ishihara;Shimpei Yamauchi
中科院分区：
文献类型：
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作者：
Junnosuke Shino;S. Ishihara;Shimpei Yamauchi
区间博弈是合作联盟博弈的一种扩展，在这种博弈中，参与人被假定面临收益的不确定性。因此，特征函数指定一个封闭的区间，而不是一个真实的数。在本文中，我们首先研究的概念，解决方案映射，解决方案的概念适用于区间游戏，通过比较它与现有的解决方案的概念称为区间解决方案的概念。然后，我们定义一个Shapley映射作为一个特定形式的解决方案映射。最后，它表明，Shapley映射可以由两种不同的公理化，这两个采用区间博弈版本的标准公理在传统的合作博弈分析，如效率，对称性，空玩家属性，可加性和可分性。
Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval, instead of a real number. In this paper, we first examine the notion of solution mapping, a solution concept applied to interval games, by comparing it with the existing solution concept called the interval solution concept. Then, we define a Shapley mapping as a specific form of the solution mapping. Finally, it is shown that the Shapley mapping can be characterized by two different axiomatizations, both of which employ interval game versions of standard axioms used in the traditional cooperative game analysis such as efficiency, symmetry, null player property, additivity and separability.