Equivalence of Strong and Coalition-Proof Nash Equilibria in Games without Spillovers
AbstractThis 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.
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Bibliographic InfoPaper provided by Universite Aix-Marseille III in its series G.R.E.Q.A.M. with number 95a39.
Length: 22 pages
Date of creation: 1995
Date of revision:
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Postal: G.R.E.Q.A.M., (GROUPE DE RECHERCHE EN ECONOMIE QUANTITATIVE D'AIX MARSEILLE), CENTRE DE VIEILLE CHARITE, 2 RUE DE LA CHARITE, 13002 MARSEILLE.
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GAME THEORY; ECONOMIC EQUILIBRIUM;
Other versions of this item:
- Michel Le Breton & Hideo Konishi & Shlomo Weber, 1996. "Equivalence of strong and coalition-proof Nash equilibria in games without spillovers (*)," Economic Theory, Springer, vol. 9(1), pages 97-113.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D62 - Microeconomics - - Welfare Economics - - - Externalities
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- 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.
- Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game," CIRED Working Papers halshs-00271464, HAL.
- Le Breton, Michel & Weber, Shlomo, 2004. "Group Formation with Heterogeneous Sets," IDEI Working Papers 288, Institut d'Économie Industrielle (IDEI), Toulouse.
- 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.
- Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer, vol. 42(2), pages 461-482, May.
- Heller, Yuval, 2008. "Ex-ante and ex-post strong correlated equilbrium," MPRA Paper 7717, University Library of Munich, Germany, revised 11 Mar 2008.
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