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The selectope for bicooperative games

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  • Bilbao, J.M.
  • Jiménez, N.
  • López, J.J.

Abstract

A bicooperative game is defined by a worth function on the set of ordered pairs of disjoint coalitions of players. The aim of this paper is to analyze the selectope for bicooperative games. This solution concept was introduced by Hammer et al. (1977) [20] and studied by Derks et al. (2000) [10] for cooperative games. We show the relations between the selectope, the core and the Weber set and obtain a characterization of almost positive bicooperative games as bicooperative games such that the core, the Weber set and the selectope coincide. Moreover, an axiomatic characterization of the elements of the selectope is obtained.

Suggested Citation

  • Bilbao, J.M. & Jiménez, N. & López, J.J., 2010. "The selectope for bicooperative games," European Journal of Operational Research, Elsevier, vol. 204(3), pages 522-532, August.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:3:p:522-532
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    References listed on IDEAS

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    1. Edward M. Bolger, 2000. "A consistent value for games with n players and r alternatives," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 93-99.
    2. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
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    4. Jean Derks & Gerard Laan & Valery Vasil’ev, 2006. "Characterizations of the Random Order Values by Harsanyi Payoff Vectors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 155-163, August.
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    6. J. Bilbao & J. Fernández & N. Jiménez & J. López, 2007. "The core and the Weber set for bicooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 209-222, October.
    7. J. Bilbao & J. Fernández & N. Jiménez & J. López, 2008. "The Shapley value for bicooperative games," Annals of Operations Research, Springer, vol. 158(1), pages 99-115, February.
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    10. Derks, J J M, 1992. "A Short Proof of the Inclusion of the Core in the Weber Set," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 149-150.
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    Cited by:

    1. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.

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