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Equivalence of strong and coalition-proof Nash equilibria in games without spillovers (*)

Author

Listed:
  • Michel Le Breton

    (GREQAM, Chateau Lafarge, Route des Milles, F-13290 Les Milles, FRANCE)

  • Hideo Konishi

    (Department of Economics, Southern Methodist University, Dallas, TX 75275-0496, USA)

  • Shlomo Weber

    (Department of Economics, Southern Methodist University, Dallas, TX 75275-0496, USA)

Abstract

This paper examines the conditions which guarantee that the set of coalition-proof Nash equilibria coincides with the set of strong Nash equilibria in the normal form games without spillovers. We find that population monotonicity properties of the payoff functions, when the payoff of a player changes monotonically when the size of the group of players choosing the same strategy increases, are crucial to obtain the equivalence of these two solution concepts. We identify the classes of games, satisfying population monotonicity properties, which yield the equivalence of the set of coalition-proof Nash equilibria and the set of strong Nash equilibria. We also provide sufficient conditions for the equivalence result even when the population monotonicity assumptions are relaxed.

Suggested Citation

  • Michel Le Breton & Hideo Konishi & Shlomo Weber, 1996. "Equivalence of strong and coalition-proof Nash equilibria in games without spillovers (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 97-113.
    • Handle: RePEc:spr:joecth:v:9:y:1996:i:1:p:97-113
    Note: Received: March 13, 1995; revised version August 15, 1995
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    Cited by:

    1. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game," Working Papers halshs-00271464, HAL.
    2. Shin-Kun Peng & Ping Wang, 2003. "Sorting by Foot: Consumable Travel-for Local Public Good and Equilibrium Stratification," IEAS Working Paper : academic research 03-A008, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    3. Heller, Yuval, 2008. "Ex-ante and ex-post strong correlated equilbrium," MPRA Paper 7717, University Library of Munich, Germany, revised 11 Mar 2008.
    4. Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 461-482, May.
    5. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
    6. Savvateev Alexey, 2004. "Achieving stability in heterogeneous societies: multi-jurisdictional structures, and redistribution policies," EERC Working Paper Series 04-13e, EERC Research Network, Russia and CIS.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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