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Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games

Author

Listed:
  • Lisa Hellerstein

    (Department of Computer Science and Engineering, New York University Tandon School of Engineering, New York, New York 11201)

  • Thomas Lidbetter

    (Department of Management Science and Information Systems, Rutgers Business School, Newark, New Jersey 07102)

  • Daniel Pirutinsky

    (Department of Management Science and Information Systems, Rutgers Business School, Newark, New Jersey 07102)

Abstract

How to Choose Between Exponentially Many Strategies, In “Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games,” L. Hellerstein, T. Lidbetter, and D. Pirutinsky consider zero-sum games between a minimizer and a maximizer, where the number of pure strategies of the minimizer is exponential in the number of pure strategies of the maximizer. Such games are frequent in the search-games literature. Solving them with standard algorithms typically takes exponential time. The authors show how to compute (approximate) solutions in polynomial time, provided that there is a polynomial time (approximate) algorithm solving the best-response problem: given a mixed (randomized) strategy of the maximizer, what is a best response of the minimizer? The paper presents both a learning approach using weight updates and an approach of solely theoretical interest based on the ellipsoid algorithm. The learning approach performs well experimentally compared with approaches in the literature. The results are applied to obtain new algorithms for solving specific search games.

Suggested Citation

  • Lisa Hellerstein & Thomas Lidbetter & Daniel Pirutinsky, 2019. "Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games," Operations Research, INFORMS, vol. 67(3), pages 731-743, May.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:3:p:731-743
    DOI: 10.1287/opre.2019.1853
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    References listed on IDEAS

    as
    1. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    2. Steve Alpern & Thomas Lidbetter, 2015. "Optimal Trade-Off Between Speed and Acuity When Searching for a Small Object," Operations Research, INFORMS, vol. 63(1), pages 122-133, February.
    3. Alpern, Steven & Lidbetter, Thomas, 2015. "Optimal trade-off between speed and acuity when searching for a small object," LSE Research Online Documents on Economics 61504, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Hellerstein, Lisa & Lidbetter, Thomas, 2023. "A game theoretic approach to a problem in polymatroid maximization," European Journal of Operational Research, Elsevier, vol. 305(2), pages 979-988.
    2. Ben Hermans & Roel Leus & Jannik Matuschke, 2022. "Exact and Approximation Algorithms for the Expanding Search Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 281-296, January.

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