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Fast Complete Algorithm for Multiplayer Nash Equilibrium

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  • Sam Ganzfried

Abstract

We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the prior fastest complete algorithm on several game classes previously studied and that its runtimes even outperform the best incomplete algorithms.

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  • Sam Ganzfried, 2020. "Fast Complete Algorithm for Multiplayer Nash Equilibrium," Papers 2002.04734, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2002.04734
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    1. Talman, A.J.J. & van der Laan, G. & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Other publications TiSEM fbe9ae2f-e01d-4eef-944c-6, Tilburg University, School of Economics and Management.
    2. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    3. Turocy, Theodore L., 2005. "A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence," Games and Economic Behavior, Elsevier, vol. 51(2), pages 243-263, May.
    4. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    5. Sam Ganzfried & Austin Nowak & Joannier Pinales, 2018. "Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game," Papers 1804.04789, arXiv.org.
    6. Sam Ganzfried & Austin Nowak & Joannier Pinales, 2018. "Successful Nash Equilibrium Agent for a Three-Player Imperfect-Information Game," Games, MDPI, vol. 9(2), pages 1-8, June.
    7. Sam Ganzfried, 2020. "Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games," Papers 2001.11165, arXiv.org, revised Dec 2023.
    8. Govindan, Srihari & Wilson, Robert, 2004. "Computing Nash equilibria by iterated polymatrix approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1229-1241, April.
    9. G. van der Laan & A. J. J. Talman & L. van der Heyden, 1987. "Simplicial Variable Dimension Algorithms for Solving the Nonlinear Complementarity Problem on a Product of Unit Simplices Using a General Labelling," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 377-397, August.
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