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A survey on algorithms for Nash equilibria in finite normal-form games

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Listed:
  • Hanyu Li
  • Wenhan Huang
  • Zhijian Duan
  • David Henry Mguni
  • Kun Shao
  • Jun Wang
  • Xiaotie Deng

Abstract

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet economics and multi-agent learning. This paper reviews various algorithms computing the Nash equilibrium and its approximation solutions in finite normal-form games from both theoretical and empirical perspectives. For the theoretical part, we classify algorithms in the literature and present basic ideas on algorithm design and analysis. For the empirical part, we present a comprehensive comparison on the algorithms in the literature over different kinds of games. Based on these results, we provide practical suggestions on implementations and uses of these algorithms. Finally, we present a series of open problems from both theoretical and practical considerations.

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  • Hanyu Li & Wenhan Huang & Zhijian Duan & David Henry Mguni & Kun Shao & Jun Wang & Xiaotie Deng, 2023. "A survey on algorithms for Nash equilibria in finite normal-form games," Papers 2312.11063, arXiv.org.
    • Handle: RePEc:arx:papers:2312.11063
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    2. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    3. Frederick Ploeg & Aart Zeeuw, 1992. "International aspects of pollution control," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 2(2), pages 117-139, March.
    4. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    5. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    6. Metrick, Andrew & Polak, Ben, 1994. "Fictitious Play in 2 x 2 Games: A Geometric Proof of Convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 923-933, October.
    7. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    8. van der Ploeg, F. & de Zeeuw, A.J., 1990. "International aspects of pollution control," Other publications TiSEM 2a1900cf-0e05-459e-8c68-a, Tilburg University, School of Economics and Management.
    9. Monderer, Dov & Sela, Aner, 1996. "A2 x 2Game without the Fictitious Play Property," Games and Economic Behavior, Elsevier, vol. 14(1), pages 144-148, May.
    10. van der Ploeg, F. & de Zeeuw, A.J., 1992. "International aspects of pollution control," Other publications TiSEM 5d08aa40-9b59-4bac-811a-b, Tilburg University, School of Economics and Management.
    11. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
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