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The average tree solution for cooperative games with communication structure

Author

Listed:
  • Herings, P.J.J.

    (Microeconomics & Public Economics)

  • van der Laan, G.

    (Externe publicaties SBE)

  • Talman, A.J.J.

    (Externe publicaties SBE)

  • Yang, Z.

    (Externe publicaties SBE)

Abstract

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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Suggested Citation

  • Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z., 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
    DOI: 10.26481/umamet.2008026
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
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    9. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
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    12. Talman, A.J.J. & Yamamoto, Y., 2008. "Average tree solution and subcore for acyclic graph games," Other publications TiSEM 47c15bd0-3911-429c-8952-7, Tilburg University, School of Economics and Management.
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    JEL classification:

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

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