Summary
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 withoutspillovers. We find thatpopulation 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aumann, R. J.: Acceptable points in general cooperative n-person games. In: Contributions to the theory of games, Vol. IV. Princeton: Princeton University Press 1959
Bernheim, D., Peleg, B., Whinston M.: Coalition-proof Nash equilibria: I concepts. Journal of Economic Theory42, 1–12 (1987)
Borm, P., Tijs, S. H.: Strategic claim games corresponding to NTU-games. Games and Economic Behavior4, 58–71 (1992)
Borm, P., Otten, G-J., Peters, H.: Core implementation in modified strong and coalition proof Nash equilibria. Tilburg University Discussion Paper, 1992
Demange, G., Henriet, D.: Sustainable oligopolies. Journal of Economic Theory54, 417–428 (1991)
Demange, G.: Intermediate preferences and stable coalition structures. Journal of Mathematical Economics23, 45–58 (1994)
Greenberg, J., Weber, S.: Multiparty equilibria under proportional representation. American Political Science Review79, 693–703 (1985)
Greenberg, J., Weber, S.: Strong Tiebout equilibrium under restricted preferences domain. Journal of Economic Theory38, 101–117 (1986)
Greenberg, J.: Deriving strong and coalition-proof Nash equilibria from an abstract system. Journal of Economic Theory49, 195–202 (1989)
Greenberg, J., Weber, S.: State coalition structures with unidimensional set of alternatives. Journal of Economic Theory60, 62–82 (1993)
Guesnerie, R., Oddou, C.: Second best taxation as a game. Journal of Economic Theory60, 67–91 (1981)
Ichiishi, T.: The cooperative nature of the firm. London: Cambridge University Press 1993
Kalai, E., Postlewaite, A., Roberts, J.: A group incentive compatible mechanism yielding core allocations. Journal of Economic Theory20, 13–22 (1979)
Kahn, C. M., Mookherjee, D.: The good, the bad and the ugly: coalition proof equilibrium in infinite games. Games and Economic Behavior4, 101–121 (1992)
Kaneko, M., Wooders, M. H.: Cores of partitioning games. Mathematical Social Sciences3, 313–327 (1982)
Konishi, H., Le Breton, M., Weber, S.: Equilibrium in a model with partial rivalry. Forthcoming Journal of Economic Theory 1995a
Konishi, H., Le Breton, M., Weber, S.: Pure strategy Nash equilibrium in games with positive externalities. Working Paper, Richard B. Johnson Center for Economic Studies at Southern Methodist University, 1995b
Le Breton, M., Owen, G., Weber, S.: Strongly balanced cooperative games. International Journal of Game Theory20, 419–427 (1992)
Peleg, B.: Game theoretic analysis of voting in committees. London: Cambridge University Press 1984
Scarf, H.: The core of an N-person game. Econometrica35, 50–69 (1967)
Thomson, W.: Population monotonic allocation rules. In: A. Barnett, M. Salles, H. Moulin and N. Schofield (eds.) Social choice, welfare and ethics. London: Cambridge University Press 1994
Wako, J.: Coalition-proofness the competitive allocations in a market with indivisible goods. Gakushuin University Discussion Paper, 1994
Author information
Authors and Affiliations
Additional information
We wish to thank Mamoru Kaneko, Akihiko Matsui, Tomoichi Shinotsuka, Benyamin Shitoviz, Tayfun Sonmez, William Thomson, the participants of the Southeastern Economic Theory Meeting in Charlottesville and the seminars at CORE and University of Tsukuba for useful discussions and comments. Our special thanks due anonymous referee for the suggestion to add a section addressing the issue of existence of a strong Nash equilibrium.
Rights and permissions
About this article
Cite this article
Konishi, H., Le Breton, M. & Weber, S. Equivalence of strong and coalition-proof Nash equilibria in games without spillovers. Econ Theory 9, 97–113 (1997). https://doi.org/10.1007/BF01213445
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01213445