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Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto

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  • Sam Ganzfried

    (Ganzfried Research, Miami Beach, FL 33139, USA)

Abstract

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games—in which the pure strategy space is (potentially uncountably) infinite—is far more challenging. Nonetheless, many real-world domains have continuous action spaces, e.g., where actions refer to an amount of time, money, or other resource that is naturally modeled as being real-valued as opposed to integral. We present a new algorithm for approximating Nash equilibrium strategies in continuous games. In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games with imperfect information. We experiment with our algorithm on a continuous imperfect-information Blotto game, in which two players distribute resources over multiple battlefields. Blotto games have frequently been used to model national security scenarios and have also been applied to electoral competition and auction theory. Experiments show that our algorithm is able to quickly compute close approximations of Nash equilibrium strategies for this game.

Suggested Citation

  • Sam Ganzfried, 2021. "Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto," Games, MDPI, vol. 12(2), pages 1-11, June.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:2:p:47-:d:566824
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    References listed on IDEAS

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    Cited by:

    1. João Ricardo Faria & Daniel Arce, 2022. "A Preface for the Special Issue “Economics of Conflict and Terrorism”," Games, MDPI, vol. 13(2), pages 1-2, April.
    2. Louis Abraham, 2023. "A Game of Competition for Risk," Working Papers hal-04112160, HAL.
    3. Louis Abraham, 2023. "A Game of Competition for Risk," Papers 2305.18941, arXiv.org.
    4. Le Zhang & Lijing Lyu & Shanshui Zheng & Li Ding & Lang Xu, 2022. "A Q-Learning-Based Approximate Solving Algorithm for Vehicular Route Game," Sustainability, MDPI, vol. 14(19), pages 1-14, September.

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