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A Nash Equilibrium in Electoral Competition Models

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Abstract

Since the introduction of better-reply security by Reny (1999), the literature studying the existence of a pure strategy Nash equilibrium (PSNE) in discontinuous games has grown substantially. In this paper, we introduce a weak notion of better-reply security, which is applicable to both quasiconcave and nonquasiconcave games. Our conditions for feeble better-reply security are simple, easy to verify and particularly useful in electoral competition games. We also provide necessary and sufficient conditions for the existence of a PSNE in a canonical electoral competition game. Finally, this paper demonstrates why a PSNE fails to exist when a particular type of discontinuity exists in a model.

Suggested Citation

  • Shino Takayama & Yuki Tamura, 2015. "A Nash Equilibrium in Electoral Competition Models," Discussion Papers Series 546, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uq2004:546
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    File URL: https://economics.uq.edu.au/files/46100/546.pdf
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    Keywords

    Noncooperative games; discontinuous payoffs; pure strategy Nash equilibrium; existence of equilibrium; better-reply security; electoral competitions;
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