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More strategies, more Nash equilibria

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Author Info
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)

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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.

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

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Date of creation: 03 Feb 2005
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Handle: RePEc:wpa:wuwpga:0502001

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Related research
Keywords: Strategic-form games; strategy spaces; Nash equilibrium; two players;

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bernheim, B Douglas & Whinston, Michael D, 1998. "Incomplete Contracts and Strategic Ambiguity," American Economic Review, American Economic Association, vol. 88(4), pages 902-32, September. [Downloadable!] (restricted)
    Other versions:
  2. Thomas Quint & Martin Shubik, 1994. "On the Number of Nash Equilibria in a Bimatrix Game," Cowles Foundation Discussion Papers 1089, Cowles Foundation, Yale University. [Downloadable!]
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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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  6. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, March. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Guillaume Haeringer & Sophie Bade & Ludovic Renou, 2006. "Bilateral Commitment," Working Papers 2006.75, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  2. 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). [Downloadable!]
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