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Asymmetric players in the Solidarity and Shapley values

Author

Listed:
  • Emilio Calvo

    (Universidad de Valencia. ERI-CES)

  • Esther Gutiérrez-López

    (Departamento de Economía Aplicada IV. Universidad del País Vasco U.P.V./E.H.U.)

Abstract

We present a general bargaining protocol between n players in the setting of coalitional games with transferable utility. We consider asymmetric players. They are endowed with di¤erent probabilities of being chosen as proposers and with di¤erent probabilities of leaving the game if o¤ers are rejected. Two particular speci…cations of this bargaining protocol yield equilibrium proposals that we refer to as weighted solidarity values and weighted Shapley values. We compare the behavior of these values when the players’ probabilities are changed. We supplement the analysis with axiomatic characterizations of both values.

Suggested Citation

  • Emilio Calvo & Esther Gutiérrez-López, 2017. "Asymmetric players in the Solidarity and Shapley values," Discussion Papers in Economic Behaviour 0217, University of Valencia, ERI-CES.
    • Handle: RePEc:dbe:wpaper:0217
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    References listed on IDEAS

    as
    1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    2. Emilio Calvo & Esther Gutiérrez, 2013. "The Shapley-Solidarity Value For Games With A Coalition Structure," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-24.
    3. Calvo, Emilio & Gutiérrez-López, Esther, 2014. "Axiomatic characterizations of the weighted solidarity values," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 6-11.
    4. Emilio Calvo, 2008. "Random marginal and random removal values," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 533-563, December.
    5. Guillermo Owen, 1968. "Communications to the Editor--A Note on the Shapley Value," Management Science, INFORMS, vol. 14(11), pages 731-731, July.
    6. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    7. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    8. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    9. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    10. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    n-person bargaining; transferable utility games; asymmetric players; solidarity value; Shapley value.;
    All these keywords.

    JEL classification:

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

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