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A globally convergent algorithm to compute all nash equilibria for n-person games

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  • Herings, P.J.J.

    (Microeconomics & Public Economics)

  • Peeters, R.J.A.P.

    (Microeconomics & Public Economics)

Abstract

In this paper we present an algorithm to compute all Nash equilibria for generic finite n-person games in normal form. The algorithm relies on decomposing the game by means of support-sets. For each support-set, the set of totally mixed equilibria of the support-restricted game can be characterized by a system of polynomial equations and inequalities. By finding all the solutions to those systems, all equilibria are found. The algorithm belongs to the class of homotopy-methods and can be easily implemented. Finally, several techniques to speed up computations are proposed. Copyright Springer Science + Business Media, Inc. 2005
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Suggested Citation

  • Herings, P.J.J. & Peeters, R.J.A.P., 2002. "A globally convergent algorithm to compute all nash equilibria for n-person games," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2002053
    DOI: 10.26481/umamet.2002053
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    References listed on IDEAS

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    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, December.
    2. C. B. Garcia & W. I. Zangwill, 1979. "Determining All Solutions to Certain Systems of Nonlinear Equations," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 1-14, February.
    3. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
    4. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    5. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, January.
    6. P. Jean-Jacques Herings & Ronald J.A.P. Peeters, 2001. "symposium articles: A differentiable homotopy to compute Nash equilibria of n -person games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 159-185.
    7. Todd R. Kaplan & John Dickhaut, "undated". "A Program for Finding Nash Equilibria," Working papers _004, University of Minnesota, Department of Economics.
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    Cited by:

    1. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 55-96, January.
    2. Natalia Novikova & Irina Pospelova, 2022. "Germeier’s Scalarization for Approximating Solution of Multicriteria Matrix Games," Mathematics, MDPI, vol. 11(1), pages 1-28, December.
    3. Felix Kubler & Karl Schmedders, 2010. "Tackling Multiplicity of Equilibria with Gröbner Bases," Operations Research, INFORMS, vol. 58(4-part-2), pages 1037-1050, August.
    4. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    5. Peixuan Li & Chuangyin Dang, 2020. "An Arbitrary Starting Tracing Procedure for Computing Subgame Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 667-687, August.
    6. Iryna Topolyan, 2013. "Existence of perfect equilibria: a direct proof," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 697-705, August.
    7. Yang Zhan & Chuangyin Dang, 2021. "Computing equilibria for markets with constant returns production technologies," Annals of Operations Research, Springer, vol. 301(1), pages 269-284, June.

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