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

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  • Gatti, J.R.J.
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    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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    File URL: http://www.econ.cam.ac.uk/research/repec/cam/pdf/cwpe0510.pdf
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    Bibliographic 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
    Date of revision:
    Handle: RePEc:cam:camdae:0510

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    Web page: http://www.econ.cam.ac.uk/index.htm

    Related research

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

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    References

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    1. Leo K. Simon and William R. Zame., 1987. "Discontinuous Games and Endogenous Sharing Rules," Economics Working Papers 8756, University of California at Berkeley.
    2. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
    3. Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
    4. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, The Center for the Study of Rationality, Hebrew University, Jerusalem.
    5. Fudenberg, Drew & Levine, David, 1986. "Limit Games and Limit Equilibria," Scholarly Articles 3350443, Harvard University Department of Economics.
    6. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
    7. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
    8. 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.
    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, Wiley Blackwell, vol. 60(4), pages 935-48, October.
    10. 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.
    11. 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.
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    Cited by:
    1. Rabia Nessah & Guoqiang Tian, 2009. "Existence of Equilibria in Discontinuous and Nonconvex Games," Levine's Working Paper Archive 814577000000000206, David K. Levine.

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