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Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game

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  • Sam Ganzfried
  • Austin Nowak
  • Joannier Pinales

Abstract

Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in two-player zero-sum games, but no guarantees in non-zero-sum games or in games with more than two players. We describe an agent that is able to defeat a variety of realistic opponents using an exact Nash equilibrium strategy in a 3-player imperfect-information game. This shows that, despite a lack of theoretical guarantees, agents based on Nash equilibrium strategies can be successful in multiplayer games after all.

Suggested Citation

  • Sam Ganzfried & Austin Nowak & Joannier Pinales, 2018. "Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game," Papers 1804.04789, arXiv.org.
    • Handle: RePEc:arx:papers:1804.04789
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    References listed on IDEAS

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    1. 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.
    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. Koller, Daphne & Megiddo, Nimrod, 1992. "The complexity of two-person zero-sum games in extensive form," Games and Economic Behavior, Elsevier, vol. 4(4), pages 528-552, October.
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    Cited by:

    1. Sam Ganzfried, 2020. "Fast Complete Algorithm for Multiplayer Nash Equilibrium," Papers 2002.04734, arXiv.org, revised Jan 2023.
    2. Sam Ganzfried, 2020. "Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games," Papers 2001.11165, arXiv.org, revised Jul 2024.

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