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Weighted Solidarity Values

Author

Listed:
  • Emilio Calvo

    (ERI-CES)

  • Esther Gutiérrez

    (Universidad del País Vasco/EHU)

Abstract

We present a noncooperative bargaining protocol among n players, applied to the setting of cooperative games in coalitional form with transferable utility. In this model, players are chosen randomly to make proposals until one is accepted unanimously, and after each proposal rejection, the probability that players leave the game increases. If after a rejection, some players withdraw the bargaining, the remaining players continue the process. We define a new family of values, called the weighted solidarity values, and we show that these values arise as the associated equilibrium payoffs of this bargaining protocol. In these values players have an altruistic behavior between them as the null player property is not satisfied.

Suggested Citation

  • Emilio Calvo & Esther Gutiérrez, 2012. "Weighted Solidarity Values," Discussion Papers in Economic Behaviour 0212, University of Valencia, ERI-CES.
    • Handle: RePEc:dbe:wpaper:0212
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    File URL: https://www.uv.es/erices/RePEc/WP/2012/0212.pdf
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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. Perez-Castrillo, D. & Wettstein, D., 1999. "Bidding for the Surplus: a Non-Cooperative Approach to the Shapley Value. ation," Papers 24-99, Tel Aviv.
    3. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    4. 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.
    5. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    6. 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.
    7. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    9. René Brink & Yukihiko Funaki & Yuan Ju, 2013. "Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 693-714, March.
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    Cited by:

    1. Radzik, Tadeusz, 2013. "Is the solidarity value close to the equal split value?," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 195-202.

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    More about this item

    Keywords

    n-person bargaining; coalitional games; altruism; 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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