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On the properties of the nucleolus of a veto game

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  • Eric Bahel

    (Virginia Polytechnic Institute and State University)

Abstract

We study the nucleolus of veto games (see Bahel in Int J Game Theory 45(3):543–566, 2016), where some players are indispensable for coalitions to achieve a positive value. We first derive some noticeable properties satisfied by the nucleolus of a veto game: for instance, veto players always receive a higher payoff than the others. In the particular case of clan games, Potters et al. (Games Econ Behav 1:275–293, 1989) provided a formula for the nucleolus. We give a condition that is necessary and sufficient for this formula to apply in a general veto game. Building on this result, we describe an intuitive adjustment process allowing to derive a generic formula for the nucleolus of a veto game.

Suggested Citation

  • Eric Bahel, 2019. "On the properties of the nucleolus of a veto game," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 221-234, December.
    • Handle: RePEc:spr:etbull:v:7:y:2019:i:2:d:10.1007_s40505-018-0155-6
    DOI: 10.1007/s40505-018-0155-6
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    References listed on IDEAS

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    1. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
    2. Vincent Feltkamp & Javier Arin, 1997. "The Nucleolus and Kernel of Veto-Rich Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 61-73.
    3. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    5. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    6. Eric Bahel, 2014. "On the core and bargaining set of a veto game," Working Papers e07-48, Virginia Polytechnic Institute and State University, Department of Economics.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU game; Veto power; Weak player; Excess; Nucleolus;
    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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