Strong equilibria in games with the lexicographical improvement property
We study a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the lexicographical improvement property (LIP) and show that, in finite games, it is equivalent to the existence of a generalized strong potential function. We use this characterization to derive existence, efficiency and fairness properties of strong equilibria (SE). As our main result, we show that an important class of games that we call bottleneck congestion games has the LIP and thus the above mentioned properties. For infinite games, the LIP does neither imply the existence of a generalized strong potential nor the existence of SE. We therefore introduce the slightly more general concept of the pairwise LIP and prove that whenever the pairwise LIP is satisfied for a continuous function, then there exists a SE. As a consequence, we show that splittable bottleneck congestion games with continuous facility cost functions possess a SE. Copyright The Author(s) 2013
Volume (Year): 42 (2013)
Issue (Month): 2 (May)
|Contact details of provider:|| Web page: http://link.springer.de/link/service/journals/00182/index.htm|
|Order Information:||Web: http://link.springer.de/orders.htm|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
- Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer, vol. 36(3), pages 379-405, September.
- repec:ner:tilbur:urn:nbn:nl:ui:12-169686 is not listed on IDEAS
- Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
- Michel Le Breton & Hideo Konishi & Shlomo Weber, 1996.
"Equivalence of strong and coalition-proof Nash equilibria in games without spillovers (*),"
Springer, vol. 9(1), pages 97-113.
- Le Breton, M. & Konishi, H. & Weber, S., 1995. "Equivalence of Strong and Coalition-Proof Nash Equilibria in Games without Spillovers," G.R.E.Q.A.M. 95a39, Universite Aix-Marseille III.
- Voorneveld, M. & Borm, P.E.M. & van Megen, F.J.C. & Tijs, S.H. & Facchini, G., 1999.
"Congestion games and potentials reconsidered,"
Other publications TiSEM
a2b8c559-8a5b-4a4a-8205-9, Tilburg University, School of Economics and Management.
- Andelman, Nir & Feldman, Michal & Mansour, Yishay, 2009. "Strong price of anarchy," Games and Economic Behavior, Elsevier, vol. 65(2), pages 289-317, March.
- Bernheim, B. Douglas & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria II. Applications," Journal of Economic Theory, Elsevier, vol. 42(1), pages 13-29, June.
- Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
- Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
- Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
- 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.
When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:42:y:2013:i:2:p:461-482. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.