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On the Openness of Unique Pure-Strategy Nash Equilibrium

Author

Listed:
  • Klis Anna A.

    (Department of Economics, Northern Illinois University, DeKalbIL 60115, USA)

Abstract

This paper investigates whether small perturbations to a game with continuous strategy spaces and unique Nash equilibrium also yields a game with unique equilibrium. The answer is affirmative for games with smooth payoffs, differentiable strict concavity in own actions, and transversal intersection of best response curves. Though intuitive for games with unique interior equilibrium, this result holds even for equilibria at the boundaries of strategy sets.

Suggested Citation

  • Klis Anna A., 2019. "On the Openness of Unique Pure-Strategy Nash Equilibrium," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(1), pages 1-9, January.
    • Handle: RePEc:bpj:bejtec:v:19:y:2019:i:1:p:9:n:14
    DOI: 10.1515/bejte-2017-0065
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    References listed on IDEAS

    as
    1. Kotchen, Matthew J., 2007. "Equilibrium existence and uniqueness in impure public good models," Economics Letters, Elsevier, vol. 97(2), pages 91-96, November.
    2. Hogan Seamus D, 2011. "A New Existence and Uniqueness Theorem for Continuous Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-28, August.
    3. Fraser, Clive D., 2012. "Nash equilibrium existence and uniqueness in a club model," Economics Letters, Elsevier, vol. 117(2), pages 496-499.
    4. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    5. repec:dau:papers:123456789/387 is not listed on IDEAS
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