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A Program for Finding Nash Equilibria

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  • Todd R. Kaplan
  • John Dickhaut

Abstract

We describe two-person simultaneous play games. First, we use a zero sum game to illustrate minimax, dominant and best response strategies. We illustrate Nash Equilbria in the Prisoner's Dilemma and the Battle of the Sexes Game, and distinguish three types of Nash Equilibria: a pure strategy, a mixed strategy, and a continuum (partially) mixed strategy. Then we introduce the program, Nash.m and use it to solve the games. We display the full code of Nash.m, and finally we discuss the performance characteristics of Nash.m.

Suggested Citation

  • Todd R. Kaplan & John Dickhaut, "undated". "A Program for Finding Nash Equilibria," Working papers _004, University of Minnesota, Department of Economics.
    • Handle: RePEc:wop:minnec:_004
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    File URL: http://www.econ.umn.edu/~todd/Nashpaper.ps
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    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
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    Cited by:

    1. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    2. Rahul Savani & Bernhard von Stengel, 2016. "Unit vector games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 7-27, March.
    3. Dickhaut, John & Kaplan, Todd R & Mukherji, Arijit, 1992. "Strategic information transmission: a mathematica tool for analysis," MPRA Paper 33869, University Library of Munich, Germany.
    4. P. Herings & Ronald Peeters, 2005. "A Globally Convergent Algorithm to Compute All Nash Equilibria for n-Person Games," Annals of Operations Research, Springer, vol. 137(1), pages 349-368, July.
    5. Papahristodoulou, Christos, 2012. "Optimal football strategies: AC Milan versus FC Barcelona," MPRA Paper 35940, University Library of Munich, Germany.
    6. Hadi Charkhgard & Martin Savelsbergh & Masoud Talebian, 2018. "Nondominated Nash points: application of biobjective mixed integer programming," 4OR, Springer, vol. 16(2), pages 151-171, June.
    7. C. Audet & S. Belhaiza & P. Hansen, 2006. "Enumeration of All the Extreme Equilibria in Game Theory: Bimatrix and Polymatrix Games," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 349-372, June.
    8. David Avis & Gabriel Rosenberg & Rahul Savani & Bernhard Stengel, 2010. "Enumeration of Nash equilibria for two-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 9-37, January.

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