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A Note on the Existence of Nash Equilibrium in Games with Discontinuous Payoffs

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Author Info
Gatti, J.R.J.
Abstract

This paper generalises the approach taken by Dasgupta & Maskin (1986) and Simon (1989) and provides necessary and sufficient conditions for the existence of pure and mixed strategy Nash equilibrium in games with continuous strategy spaces and discontinuous payoff functions. The conditions can be applied widely, and examples for existence of pure strategy and monotonic equilibria in First-Price auctions are provided. The conditions are also appropriate for ensuring that computer generated equilibrium solutions can be extended to continuous strategy spaces.

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Publisher Info
Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0510.

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Length: 28
Date of creation: Feb 2005
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Handle: RePEc:cam:camdae:0510

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Related research
Keywords: Nash Equilibrium; Discontinuous Payoff Function; First-price Auctions;

Find related papers by JEL classification:
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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.:
  1. Fudenberg, Drew & Levine, David, 1986. "Limit games and limit equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 261-279, April. [Downloadable!] (restricted)
    Other versions:
  2. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
    Other versions:
  3. 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.
  4. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Blackwell Publishing, vol. 54(4), pages 569-97, October. [Downloadable!] (restricted)
  5. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-72, July. [Downloadable!] (restricted)
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  6. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 1-26, January. [Downloadable!] (restricted)
  7. Tian, Guoqiang, 1992. "Existence of equilibrium in abstract economies with discontinuous payoffs and non-compact choice spaces," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 379-388. [Downloadable!] (restricted)
  8. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 27-41, January. [Downloadable!] (restricted)
  9. 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, Blackwell Publishing, vol. 60(4), pages 935-48, October. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
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Cited by:
(explanations, 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.)

  1. Rabia Nessah & Guoqiang Tian, 2009. "Existence of Equilibria in Discontinuous and Nonconvex Games," Levine's Working Paper Archive 814577000000000206, David K. Levine. [Downloadable!]
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