凸性
夏普里值
数学
随机博弈
树(集合论)
芯(光纤)
图形
数理经济学
组合数学
解决方案概念
博弈树
组合博弈论
博弈论
离散数学
重复博弈
计算机科学
经济
金融经济学
电信
作者
P. Jean‐Jacques Herings,Gerard van der Laan,A.J.J. Talman,Zaifu Yang
标识
DOI:10.1016/j.geb.2009.10.002
摘要
We study cooperative games with communication structure, represented by an undirected graph. Players in the game are able to cooperate only if they can form a network in the graph. A single-valued solution, the average tree solution, is proposed for this class of games. The average tree solution is defined to be the average of all these payoff vectors. It is shown that if a game has a complete communication structure, then the proposed solution coincides with the Shapley value, and that if the game has a cycle-free communication structure, it is the solution proposed by Herings, van der Laan and Talman in 2008. We introduce the notion of link-convexity, under which the game is shown to have a non-empty core and the average tree solution lies in the core. In general, link-convexity is weaker than convexity. For games with a cycle-free communication structure, link-convexity is even weaker than super-additivity.
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