Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T07:18:43.467Z Has data issue: false hasContentIssue false
  • English
  • Français

Complementarities and the existence of strong Berge equilibrium

Published online by Cambridge University Press:  30 April 2014

Kerim Keskin  and
H. Çağrı Sağlam
Kerim Keskin
Affiliation:
Department of Economics, Bilkent University, 06800 Ankara, Turkey. kerim@bilkent.edu.tr
H. Çağrı Sağlam
Affiliation:
Department of Economics, Bilkent University, 06800 Ankara, Turkey. kerim@bilkent.edu.tr
Get access

Abstract

This paper studies the existence and the order structure of strong Berge equilibrium, a refinement of Nash equilibrium, for games with strategic complementarities à la strong Berge. It is shown that the equilibrium set is a nonempty complete lattice. Moreover, we provide a monotone comparative statics result such that the greatest and the lowest equilibria are increasing.

Keywords

Strong Berge equilibriumrefinementgames with strategic complementaritiesfixed point theorysupermodularity
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 3 , July 2014 , pp. 373 - 379
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

C. Berge, Théorie Générale des Jeux à n Personnes, Gautier Villars, Paris (1957).
Nash, J.F., Non-cooperative games. Annal. Math. 54 (1951) 286–295. Google Scholar
Aumann, R., Acceptable points in a general cooperative n-person games. in Contributions to the Theory of Games IV. Annal. Math. Study 40 (1959) 287–324. Google Scholar
R. Nessah, M. Larbani and T. Tazdaït, Strong Berge equilibrium and strong Nash equilibrium: Their relation and existence, in Game Theory Appl., edited by L.A. Petrosjan and V.V. Mazalov. Vol. 15. Nova Science Publishers (2012) 165–180.
Larbani, M. and Nessah, R., Sur l’équilibre fort selon Berge. RAIRO Oper. Res. 35 (2001) 439–451. Google Scholar
Abalo, K.Y. and Kostreva, M.M., Intersection theorems and their applications to Berge equilibria. Appl. Math. Comput. 182 (2006) 1840–1848. Google Scholar
Deghdak, M. and Florenzano, M., On the existence of Berge’s strong equilibrium. Int. Game Theory Rev. 13 (2011) 325–340. Google Scholar
Zhou, L., The set of Nash equilibria of a supermodular game is a complete lattice. Games Econ. Behavior 7 (1994) 295–300. Google Scholar
Echenique, F., A short and constructive proof of Tarski’s fixed-point theorem. Int. J. Game Theory 33 (2005) 215–218. Google Scholar
D.M. Topkis, Supermodularity and Complementarity, Princeton University Press, Princeton (1998).
Vives, X., Complementarities and games: New developments. J. Econ. Literature 43 (2005) 437–479. Google Scholar
R.W. Cooper, Coordination Games: Complementarities and Macroeconomics, Cambridge University Press, Cambridge (1999).