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].
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Date of creation: Jun 2012
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Discontinuous games; Nash equilibrium; Reny equilibrium; better-reply security; endogenous sharing rule; quasi equilibrium; finite deviation equilibrium; symmetric games.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-23 (All new papers)
- NEP-GTH-2012-07-23 (Game Theory)
- NEP-HPE-2012-07-23 (History & Philosophy of Economics)
- NEP-MIC-2012-07-23 (Microeconomics)
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- 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.
- 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.
- 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.
- 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.
- Rida Laraki & Eilon Solan & Nicolas Vieille, 2003.
"Continuous-time Games of Timing,"
1363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
- 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.
- 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.
- Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
- 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 Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, vol. 48(1), pages 17-29, September.
- 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., 2005. "Non-Existence of Equilibrium in Vickrey, Second-Price, and English Auctions," Working Papers 1241, California Institute of Technology, Division of the Humanities and Social Sciences.
- Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
- 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.
- 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.
- 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.
- 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.
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