The Average Tree Solution for Cooperative Games with Communication Structure
The Average Tree Solution for Cooperative Games with Communication Structure
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DOI：
10.2139/ssrn.1265003
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发表时间：
2008-09
期刊：
影响因子：
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通讯作者：
P. Herings;G. van der Laan;Dolf Talman;Zaifu Yang
中科院分区：
文献类型：
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作者：
P. Herings;G. van der Laan;Dolf Talman;Zaifu Yang
我们研究了具有通信结构的合作博弈，用无向图表示。游戏中的玩家只有在图中形成网络时才能合作。一个单值的解决方案，平均树的解决方案，提出了这类游戏。平均树解被定义为所有这些收益向量的平均值。结果表明，如果博弈具有完全的通信结构，则所提出的解与Shapley值一致;如果博弈具有无圈的通信结构，则所提出的解是Herings，货车der Laan和Talman在2008年提出的解.我们引入了链接凸性的概念，在此基础上，游戏被证明有一个非空的核心和平均树的解决方案在于核心。一般来说，链路凸性比凸性弱。对于具有无环通信结构的博弈，链接凸性甚至比超可加性更弱。
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.