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The Zero Regrets Algorithm: Optimizing over Pure Nash Equilibria via Integer Programming

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  • Gabriele Dragotto

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

  • Rosario Scatamacchia

    (Dipartimento di Ingegneria Gestionale e della Produzione, Politecnico di Torino, 10129 Torino, Italy)

Abstract

Designing efficient algorithms to compute Nash equilibria poses considerable challenges in algorithmic game theory and optimization. In this work, we employ integer programming techniques to compute Nash equilibria in integer programming games, a class of simultaneous and noncooperative games in which each player solves a parameterized integer program. We introduce zero regrets, a general and efficient cutting-plane algorithm to compute, enumerate, and select Nash equilibria. Our framework leverages the concept of equilibrium inequality, an inequality valid for any Nash equilibrium, and the associated equilibrium separation oracle. We evaluate our algorithmic framework on a wide range of practical and methodological problems from the literature, providing a solid benchmark against the existing approaches.

Suggested Citation

  • Gabriele Dragotto & Rosario Scatamacchia, 2023. "The Zero Regrets Algorithm: Optimizing over Pure Nash Equilibria via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1143-1160, September.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:5:p:1143-1160
    DOI: 10.1287/ijoc.2022.0282
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    References listed on IDEAS

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