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The Shapley Valuation Function for Strategic Games in which Players Cooperate

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  • Luisa Carpente
  • Balbina Casas-Méndez
  • Ignacio García-Jurado
  • Anne Nouweland

Abstract

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lower-value based method to associate coalitional games with strategic games that was introduced in Carpente et al. (2005). We discuss axiomatic characterizations of the Shapley valuation function. Copyright Springer-Verlag 2006

Suggested Citation

  • Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2006. "The Shapley Valuation Function for Strategic Games in which Players Cooperate," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 435-442, July.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:3:p:435-442
    DOI: 10.1007/s00186-005-0028-2
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    References listed on IDEAS

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    1. Norde, Henk & Voorneveld, Mark, 2004. "Characterizations of the value of matrix games," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 193-206, September.
    2. Montero, M.P., 2000. "Endogenous coalition formation and bargaining," Other publications TiSEM 5e5fcfcf-8c30-4856-a2e8-4, Tilburg University, School of Economics and Management.
    3. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    4. Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne van den Nouweland, 2005. "Values for strategic games in which players cooperate," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 397-419, September.
    5. van Damme, E.E.C., 2002. "Game theory and the market," Other publications TiSEM b167b13f-ef75-4003-b410-4, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Ignacio García-Jurado, 2008. "Comments on: Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 51-53, July.

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