On the existence of pure-strategy perfect equilibrium in discontinuous games
AbstractWe provide sufficient conditions for a (possibly) discontinuous normal-form game to possess a pure-strategy trembling-hand perfect equilibrium. We first show that compactness, continuity, and quasiconcavity of a game are too weak to warrant the existence of a pure-strategy perfect equilibrium. We then identify two classes of games for which the existence of a pure-strategy perfect equilibrium can be established: (1) the class of compact, metric, concave games satisfying upper semicontinuity of the sum of payoffs and a strengthening of payoff security; and (2) the class of compact, metric games satisfying upper semicontinuity of the sum of payoffs, strengthenings of payoff security and quasiconcavity, and a notion of local concavity and boundedness of payoff differences on certain subdomains of a player's payoff function. Various economic games illustrate our results.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 71 (2011)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/622836
Pure-strategy trembling-hand perfect equilibrium Infinite normal-form game Selten perturbation Discontinuous game Quasiconcave game Payoff security;
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.:
- 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.
- Novshek, William., 1984.
"On the Existence of Cournot Equilibrium,"
517, California Institute of Technology, Division of the Humanities and Social Sciences.
- Edward P. Lazear & Sherwin Rosen, 1979.
"Rank-Order Tournaments as Optimum Labor Contracts,"
NBER Working Papers
0401, National Bureau of Economic Research, Inc.
- Bester, Helmut, 1992.
"Bertrand Equilibrium in a Differentiated Duopoly,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 433-48, May.
- Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-43, November.
- Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
- Oriol Carbonell-Nicolau & Richard McLean, 2012.
"Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement,"
Departmental Working Papers
201206, Rutgers University, Department of Economics.
- Oriol Carbonell-Nicolau & Richard McLean, 2013. "Approximation results for discontinuous games with an application to equilibrium refinement," Economic Theory, Springer, vol. 54(1), pages 1-26, September.
- Oriol Carbonell-Nicolau & Richard McLean, 2011. "Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement," Departmental Working Papers 201128, Rutgers University, Department of Economics.
- Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
- Oriol Carbonell-Nicolau & Richard McLean, 2011.
"Refinements of Nash equilibrium in potential games,"
Departmental Working Papers
201125, Rutgers University, Department of Economics.
- Carbonell-Nicolau, Oriol & McLean, Richard P., 0. "Refinements of Nash equilibrium in potential games," Theoretical Economics, Econometric Society.
- Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, Open Access Journal, vol. 2(3), pages 235-256, July.
- Oriol Carbonell-Nicolau & Richard McLean, 2012. "On Equilibrium Refinement in Supermodular Games," Departmental Working Papers 201207, Rutgers University, Department of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If references are entirely missing, you can add them using this form.