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Values and potential of games with cooperation structure

Author

Listed:
  • Jesßs-Mario Bilbao

    (E. S. Ingenieros, University of Seville, Camino de los Descubrimientos, 41092 Sevilla, Spain)

Abstract

Games with cooperation structure are cooperative games with a family of feasible coalitions, that describes which coalitions can negotiate in the game. We study a model of cooperation structure and the corresponding restricted game, in which the feasible coalitions are those belonging to a partition system. First, we study a recursive procedure for computing the Hart and Mas-Colell potential of these games and we develop the relation between the dividends of Harsanyi in the restricted game and the worths in the original game. The properties of partition convex geometries are used to obtain formulas for the Shapley and Banzhaf values of the players in the restricted game $v^{ \cal L}$, in terms of the original game v. Finally, we consider the Owen multilinear extension for the restricted game.

Suggested Citation

  • Jesßs-Mario Bilbao, 1998. "Values and potential of games with cooperation structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 131-145.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:1:p:131-145
    Note: Received April 1996/Revised version February 1997/Final version July 1997
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    Citations

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    Cited by:

    1. Takao Asano & Hiroyuki Kojima, 2014. "Modularity and monotonicity of games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 29-46, August.
    2. Algaba, A. & Bilbao, J.M. & Borm, P.E.M., 1999. "The Myerson Value for Union Stable Systems," Research Memorandum 773, Tilburg University, School of Economics and Management.
    3. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 0000. "The Restricted Core for Totally Positive Games with Ordered Players," Tinbergen Institute Discussion Papers 09-038/1, Tinbergen Institute.

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