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More strategies, more Nash equilibria

  • Sophie Bade

    (Department of Economics, Penn State University)

  • Guillaume Haeringer

    (Department d'Economia i d'Historia Economica, Universitat Autonoma de Barcelona)

  • Ludovic Renou

    (University of Adelaide, School of Economics)

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.

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Paper provided by EconWPA in its series Game Theory and Information with number 0502001.

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Date of creation: 03 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpga:0502001
Note: Type of Document - pdf
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  1. Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
  2. B. Douglas Bernheim & Michael D. Whinston, 1997. "Incomplete Contracts and Strategic Ambiguity," Harvard Institute of Economic Research Working Papers 1787, Harvard - Institute of Economic Research.
  3. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
  4. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
  5. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
  6. Thomas Quint & Martin Shubik, 1994. "On the Number of Nash Equilibria in a Bimatrix Game," Cowles Foundation Discussion Papers 1089, Cowles Foundation for Research in Economics, Yale University.
  7. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
  8. McLennan, A., 1999. "The Expected Number of Nash Equilibria of a Normal Form Game," Papers 306, Minnesota - Center for Economic Research.
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