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Quasi-Cores in Bargaining Sets

Author

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  • Ken-Ichi Shimomura

    (School of International Public Policy, Osaka University, Toyonaka, Osaka 560, Japan)

Abstract

We propose a nonempty-valued subsolution of the Mas-Colell Bargaining Set on the class of TU games satisfying grand coalition zero-monotonicity, a weaker condition than superadditivity, zero-monotonicity and balancedness. The subsolution is a slight modification of the Shapley-Shubik Quasi-Core. The Zhou Bargaining Set is a refinement of the Mas-Colell Bargaining Set. We also give a nonempty-valued subsolution of the Zhou Bargaining Set on the class of all TU games satisfying grand coalition superadditivity, a weaker condition than superadditivity and balancedness. This subsolution is a modification of the Zhou Bargaining Set which is described by excesses. These results are examined for TU games with coalition structures.

Suggested Citation

  • Ken-Ichi Shimomura, 1997. "Quasi-Cores in Bargaining Sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 283-302.
    • Handle: RePEc:spr:jogath:v:26:y:1997:i:3:p:283-302
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    Cited by:

    1. Yves Breitmoser, 2012. "Proto-coalition bargaining and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 581-599, November.
    2. Josep Izquierdo & Carles Rafels, 2012. "A characterization of convex TU games by means of the Mas-Colell bargaining set (à la Shimomura)," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 381-395, May.
    3. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.
    4. Junichi Minagawa, 2012. "On the instability of competitive equilibrium: a further example," Economics Bulletin, AccessEcon, vol. 32(1), pages 80-85.
    5. Einy, Ezra & Holzman, Ron & Monderer, Dov, 1999. "On the Least Core and the Mas-Colell Bargaining Set," Games and Economic Behavior, Elsevier, vol. 28(2), pages 181-188, August.
    6. Josep M Izquierdo & Carles Rafels, 2012. "On the coincidence of the core and the bargaining sets," Economics Bulletin, AccessEcon, vol. 32(3), pages 2035-2043.

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