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The Average Tree Solution for Cooperative Games with Communication Structure

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  • Herings P. Jean-Jacques
  • Laan Gerard van der
  • Talman Dolf
  • Yang Zaifu

    (METEOR)

Abstract

We study cooperative games with communication structure, represented by an undirectedgraph. 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 ofgames. Given the graph structure we define a collection of spanning trees, where eachspanning tree specifies a particular way by which players communicate and determines a payoff vector of marginal contributions of all the players. The average tree solution is defined to be the average of all these payoff vectors. It is shown that if a game has acomplete communication structure, then the proposed solution coincides with the Shapleyvalue, and that if the game has a cycle-free communication structure, it is the solutionproposed by Herings, van der Laan and Talman (2008). We introduce the notion of linkconvexity, 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.

Suggested Citation

  • Herings P. Jean-Jacques & Laan Gerard van der & Talman Dolf & Yang Zaifu, 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Research Memorandum 026, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2008026
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    References listed on IDEAS

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    Keywords

    operations research and management science;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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