Efficient extensions of communication values
Efficient extensions of communication values
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DOI：
10.1007/s10479-017-2661-6
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发表时间：
2017-10
影响因子：
4.8
通讯作者：
S. Béal;André Casajus;Frank Huettner
中科院分区：
文献类型：
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作者：
S. Béal;André Casajus;Frank Huettner
我们研究了通过通信图丰富的可转移效用博弈的值。最著名的这些值是组件有效的，并以某些删除链接属性为特征。我们研究这些值的有效扩展：对于给定的组件效率值，我们寻找(i)满足效率的值，（ii）满足原始组件效率值下面的链接删除属性，以及（iii）在底层图连接时与原始组件效率值重合。b<s:1>等人（Soc Choice Welf 45:819-827, 2015）证明Myerson值（Myerson in Math Oper Res 2:22 25 - 229, 1977）允许一个唯一的有效扩展，该扩展由van den Brink等人（Econ Lett 117:786-789, 2012）引入。我们通过证明平均树解（Herings et al. in Games Econ Behav 62:77-92, 2008）和补偿解（bsamal et al. in Int J Game Theory 41:157-178, 2012b）具有相似的唯一有效扩展，并且不存在位置值的有效扩展（Meessen in Communication Games, 1988; Borm et al. in SIAM J Discrete Math 5:305-320, 1992）来进行这条研究线。作为副产物，我们得到了平均树解和补偿解的新性质，以及它们的有效推广。
We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some deletion link property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal et al. (Soc Choice Welf 45:819–827, 2015) prove that the Myerson value (Myerson in Math Oper Res 2:225–229, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (Econ Lett 117:786–789, 2012). We pursue this line of research by showing that the average tree solution (Herings et al. in Games Econ Behav 62:77–92, 2008) and the compensation solution (Béal et al. in Int J Game Theory 41:157–178, 2012b) admit similar unique efficient extensions, and that there exists no efficient extension of the position value (Meessen in Communication games, 1988; Borm et al. in SIAM J Discrete Math 5:305–320, 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions.