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Reduced games and egalitarian solutions

Author

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  • Francesc Llerena

    (Universitat Rovira i Virgili-CREIP)

  • Llúcia Mauri

    (Universitat Rovira i Virgili-CREIP)

Abstract

For a class of reduced games satisfying a monotonicity property, we introduce a family of set-valued solution concepts based on egalitarian considerations and consistency principles, and study its relation with the core. Regardless of the reduction operation we consider, the intersection between both sets is either empty or a singleton containing the lexmax solution Arin et al. (Math Soc Sci 46:327–345, 2003). This result induces a procedure for computing the lexmax solution for a class of games that contains games with large core Sharkey (Int J Game Theory 11:175–182, 1982).

Suggested Citation

  • Francesc Llerena & Llúcia Mauri, 2016. "Reduced games and egalitarian solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1053-1069, November.
    • Handle: RePEc:spr:jogath:v:45:y:2016:i:4:d:10.1007_s00182-015-0504-8
    DOI: 10.1007/s00182-015-0504-8
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    References listed on IDEAS

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    8. Izquierdo, Josep M. & Llerena, Francesc & Rafels, Carles, 2005. "Sequentially compatible payoffs and the core in TU-games," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 318-330, November.
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    12. Javier Arin & Jeroen Kuipers & Dries Vermeulen, 2008. "An axiomatic approach to egalitarianism in TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 565-580, December.
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    Citations

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    Cited by:

    1. Dietzenbacher, Bas, 2019. "The Procedural Egalitarian Solution and Egalitarian Stable Games," Discussion Paper 2019-007, Tilburg University, Center for Economic Research.
    2. Takafumi Otsuka, 2020. "Egalitarian solution for games with discrete side payment," Papers 2003.10059, arXiv.org.
    3. Bas Dietzenbacher & Elena Yanovskaya, 2021. "Consistency of the equal split-off set," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 1-22, March.
    4. Dietzenbacher, Bas, 2020. "Monotonicity and Egalitarianism (revision of CentER DP 2019-007)," Discussion Paper 2020-003, Tilburg University, Center for Economic Research.
    5. Dietzenbacher, Bas, 2021. "Monotonicity and egalitarianism," Games and Economic Behavior, Elsevier, vol. 127(C), pages 194-205.

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    More about this item

    Keywords

    Cooperative game; Reduced games; Core; Lexmax solution;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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