Abstract
Strategic games are considered where the players derive their utilities from participation in certain “processes”. Two subclasses consisting exclusively of potential games are singled out. In the first, players choose where to participate, but there is a unique way of participation, the same for all players. In the second, the participation structure is fixed, but each player may have an arbitrary set of strategies. In both cases, the players sum up the intermediate utilities; thus the first class essentially coincides with that of congestion games. The necessity of additivity in each case is proven.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bogomolnaia A, Jackson MO (2002) The stability of hedonic coalition structures. Games Econ Behav 38:201–230
Debreu G (1960) Topological methods in cardinal utility. In: Arrow KJ, Karlin S, Suppes P (eds) Mathematical methods in social sciences. Stanford University Press, Stanford, pp 16–26
Fishburn PC (1970) Utility theory for decision making. Wiley, New York
Germeier YuB, Vatel’ IA (1974) On games with a hierarchical vector of interests. Izvestiya Akademii Nauk SSSR, Tekhnicheskaya Kibernetika, 3:54–69. (in Russian; English translation in Engineering Cybernetics, V.12)
Gorman WM (1968) The structure of utility functions. Rev Econ Stud 35:367–390
Holland G (2000) On the existence of a pure strategy Nash equilibrium in group formation games. Econ Lett 66:283–287
Holzman R, Law-Yone N (1997) Strong equilibrium in congestion games. Games Econ Behav 21:85–101
Konishi H, Le Breton M, Weber S (1997a) Equilibria in a model with partial rivalry. J Econ Theory 72:225–237
Konishi H, Le Breton M, Weber S (1997b) Pure strategy Nash equilibrium in a group formation game with positive externalities. Games Econ Behav 21:161–182
Kukushkin NS (1994) A condition for the existence of a Nash equilibrium in games with public and private objectives. Games Econ Behav 7:177–192
Kukushkin NS (1997) An existence result for coalition-proof equilibrium. Econ Lett 57:269–273
Kukushkin NS (2004) Acyclicity of improvements in games with common intermediate objectives. Russian Academy of Sciences, Dorodnicyn Computing Center, Moscow. Available from http://www.ccas.ru/mmes/mmeda/ququ/Common3.pdf
Kukushkin NS, Men’shikov IS, Men’shikova OR, Moiseev NN (1985) Stable compromises in games with structured payoffs. Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki 25:1761–1776. (in Russian; English translation in USSR Computational Mathematics and Mathematical Physics, V.25)
McManus M (1964) Equilibrium, number and size in Cournot oligopoly. Yorkshire Bull Econ Soc Res 16:68–75
Milchtaich I (1996) Congestion games with player-specific payoff functions. Games Econ Behav 13:111–124
Monderer D, Shapley LS (1996) Potential games. Games Econ Behav 14:124–143
Rosenthal RW (1973) A class of games possessing pure-strategy Nash equilibria. Int J Game Theory 2:65–67
Voorneveld M, Borm P, Megen F, Tijs S, Facchini G (1999) Congestion games and potentials reconsidered. Int Game Theory Rev 1:283–299
Voorneveld M, Norde H (1996) A characterization of ordinal potential games. Games Econ Behav 19:235–242
Author information
Authors and Affiliations
Corresponding author
Additional information
Financial support from Presidential Grants for the State Support of the Leading Scientific Schools (NSh-1843.2003.01 and NSh-5379.2006.1), the Russian Foundation for Basic Research (grant 05-01-00942), the Spanish Ministry of Education (project SEJ2004-00968), and the Lady Davis Foundation (a fellowship at the Technion, Haifa) is acknowledged. I thank Francisco Marhuenda and Dov Monderer, respectively, for procuring the last two grants. My deepest gratitude and apology are due to an anonymous referee, who carefully read two versions of the paper, suggested several improvements, and uncovered several errors, including a wrong formulation of Theorem 1. Finally, I apologize to Mikhail Gorelov, who had warned me that something was wrong with the theorem (unfortunately, I failed to pay proper attention).
Rights and permissions
About this article
Cite this article
Kukushkin, N.S. Congestion games revisited. Int J Game Theory 36, 57–83 (2007). https://doi.org/10.1007/s00182-007-0090-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-007-0090-5