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More Strategies, More Nash Equilibria

Author

Listed:
  • Sophie Bade

    (Department of Economics, Penn State University)

  • Guillaume Haeringer

    (Department of Economics, Universitat Autonoma de Barcelona)

  • Ludovic Renou

    (School of Economics, University of Adelaide)

Abstract

This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two-player nice games, i.e., games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions, assumptions met by many economic models. We then show that the sufficient conditions for Theorem to hold are tight.

Suggested Citation

  • Sophie Bade & Guillaume Haeringer & Ludovic Renou, 2005. "More Strategies, More Nash Equilibria," School of Economics and Public Policy Working Papers 2005-01, University of Adelaide, School of Economics and Public Policy.
    • Handle: RePEc:adl:wpaper:2005-01
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    File URL: https://media.adelaide.edu.au/economics/papers/doc/wp2005-01.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Pierre Courtois & Guillaume Haeringer, 2005. "The Making of International Environmental Agreements," UFAE and IAE Working Papers 652.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    2. Pierre Courtois & Guillaume Haeringer, 2012. "Environmental cooperation: ratifying second-best agreements," Public Choice, Springer, vol. 151(3), pages 565-584, June.
    3. Klaus Kultti & Hannu Salonen & Hannu Vartiainen, 2011. "Distribution of pure Nash equilibria in n-person games with random best replies," Discussion Papers 71, Aboa Centre for Economics.
    4. Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
    5. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2009. "Bilateral commitment," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1817-1831, July.

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    More about this item

    Keywords

    strategic-form games; strategy spaces; Nash equilibrium; two players;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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