A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games
AbstractSeveral relaxations of Nash equilibrium are shown to exist in strategic games with discontinuous payoff functions. Those relaxations are used to extend and unify several recent results and link Reny's better-reply security condition [Reny, P.J. (1999). On the existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games] to Simon-Zame's endogenous tie-breaking rules [Simon, L.K. and Zame, W.R. (1990). Discontinuous Games and Endogenous Sharing Rules].
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 InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 12040.
Length: 25 pages
Date of creation: Jun 2012
Date of revision:
Discontinuous games; Nash equilibrium; Reny equilibrium; better-reply security; endogenous sharing rule; quasi equilibrium; finite deviation equilibrium; symmetric games.;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-14 (All new papers)
- NEP-GTH-2012-07-14 (Game Theory)
- NEP-HPE-2012-07-14 (History & Philosophy of Economics)
- NEP-MIC-2012-07-14 (Microeconomics)
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.:
- Carmona, Guilherme, 2008.
"An Existence Result for Discontinuous Games,"
FEUNL Working Paper Series
wp530, Universidade Nova de Lisboa, Faculdade de Economia.
- Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
- Rida Laraki & Eilon Solan & Nicolas Vieille, 2003.
"Continuous-time Games of Timing,"
1363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jackson, Matthew O., 2005.
"Non-Existence of Equilibrium in Vickrey, Second-Price, and English Auctions,"
1241, California Institute of Technology, Division of the Humanities and Social Sciences.
- Matthew Jackson, 2009. "Non-existence of equilibrium in Vickrey, second-price, and English auctions," Review of Economic Design, Springer, vol. 13(1), pages 137-145, April.
- Jackson, Matthew O. & Jeroen Swinkels, 2004.
"Existence of Equilibrium in Single and Double Private Value Auctions,"
1192, California Institute of Technology, Division of the Humanities and Social Sciences.
- Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, 01.
- Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
- Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 935-48, October.
- Fang, Hanming & Morris, Stephen, 2006.
"Multidimensional private value auctions,"
Journal of Economic Theory,
Elsevier, vol. 126(1), pages 1-30, January.
- Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Econometric Society 2004 North American Winter Meetings 174, Econometric Society.
- Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Yale School of Management Working Papers ysm387, Yale School of Management.
- Hanming Fang & Stephen Morris, 2003. "Multidimensional Private Value Auctions," Cowles Foundation Discussion Papers 1423, Cowles Foundation for Research in Economics, Yale University.
- Hanming Fang, 2004. "Multidimensional Private Value Auctions," Theory workshop papers 121473000000000021, UCLA Department of Economics.
- Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
- Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, vol. 48(1), pages 17-29, September.
- Kim, Jinwoo & Che, Yeon-Koo, 2004. "Asymmetric information about rivals' types in standard auctions," Games and Economic Behavior, Elsevier, vol. 46(2), pages 383-397, February.
- Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
- 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.
- Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
- Leo K. Simon and William R. Zame., 1987.
"Discontinuous Games and Endogenous Sharing Rules,"
Economics Working Papers
8756, University of California at Berkeley.
- Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, 09.
- Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
- Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
- Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lucie Label).
If references are entirely missing, you can add them using this form.