A general structure theorem for the Nash equilibrium correspondence
Games and Economic Behavior, 2009, vol. 66, issue 2, 950-958
I consider n-person normal form games where the strategy set of each player is a non-empty compact convex subset of an Euclidean space, and the payoff function of player i is continuous in joint strategies and continuously differentiable and concave in the player i's strategy. No further restrictions (such as multilinearity of the payoff functions or the requirement that the strategy sets be polyhedral) are imposed. I demonstrate that the graph of the Nash equilibrium correspondence on this domain is homeomorphic to the space of games. This result generalizes a well-known structure theorem in [Kohlberg, E., Mertens, J.-F., 1986. On the strategic stability of equilibria. Econometrica 54, 1003-1037]. It is supplemented by an extension analogous to the unknottedness theorems in [Demichelis S., Germano, F., 2000. Some consequences of the unknottedness of the Walras correspondence. J. Math. Econ. 34, 537-545; Demichelis S., Germano, F., 2002. On (un)knots and dynamics in games. Games Econ. Behav. 41, 46-60]: the graph of the Nash equilibrium correspondence is ambient isotopic to a trivial copy of the space of games.
Keywords: Nash; equilibrium; correspondence (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6) Track citations by RSS feed
Downloads: (external link)
Full text for ScienceDirect subscribers only
Working Paper: A general structure theorem for the nash equilibrium correspondence (2006)
Working Paper: A general structure theorem for the nash equilibrium correspondence (2004)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:66:y:2009:i:2:p:950-958
Access Statistics for this article
Games and Economic Behavior is currently edited by E. Kalai
More articles in Games and Economic Behavior from Elsevier
Bibliographic data for series maintained by Catherine Liu ().