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The B.E. Journal of Theoretical Economics

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On the Openness of Unique Pure-Strategy Nash Equilibrium

Anna A. KlisORCID iD: http://orcid.org/0000-0001-5684-2870
Published Online: 2018-01-04 | DOI: https://doi.org/10.1515/bejte-2017-0065


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.

Keywords: unique Nash equilibrium; pure strategies; open condition; differentiable strict concavity; transversal; game theory; univalence


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Published Online: 2018-01-04

Citation Information: The B.E. Journal of Theoretical Economics, 20170065, ISSN (Online) 1935-1704, DOI: https://doi.org/10.1515/bejte-2017-0065.

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