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Reconstructing a simple game from a uniparametric family of allocations

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  • Rafael Amer
  • José Giménez
  • Antonio Magaña

Abstract

Several relationships between simple games and a particular type of solutions for cooperative games are studied in this paper. These solutions belong to the set of semivalues and they are related to a unique parameter that explicitly provides their weighting coefficients. Through the allocations offered by this family of solutions, so-called binomial semivalues, and also from their respective potentials, some characteristics of the simple games can be recovered. The paper analyzes the capacity of binomial semivalues to summarize the structure of simple games, and, moreover, a property of separation among simple games is given. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Rafael Amer & José Giménez & Antonio Magaña, 2013. "Reconstructing a simple game from a uniparametric family of allocations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 505-523, October.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:3:p:505-523
    DOI: 10.1007/s11750-011-0194-8
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    References listed on IDEAS

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    1. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
    2. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. Rafael Amer & José Miguel giménez, 2003. "Modification of Semivalues for Games with Coalition Structures," Theory and Decision, Springer, vol. 54(3), pages 185-205, May.
    4. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    5. Calvo, Emilio & Santos, Juan Carlos, 1997. "Potentials in cooperative TU-games," Mathematical Social Sciences, Elsevier, vol. 34(2), pages 175-190, October.
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    More about this item

    Keywords

    Game theory; Simple game; Semivalue; Potential; Banzhaf value; 91A12;
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