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<p>We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, <i>i.e.</i>, simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We prove that using absolute approximations of the players’ objective functions and then computing its Nash equilibria is equivalent to computing approximate Nash equilibria where the approximation factor is doubled. In practice, we propose an algorithm to approximate the players’ objective functions via piecewise linear approximations. The numerical experiments on a cybersecurity investment game combined with a detailed analysis of the results show the computational effectiveness of our approach.</p>

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Computing approximate Nash equilibria for integer programming games

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月31日

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  • Aloïs Duguet,
  • Margarida Carvalho,
  • Gabriele Dragotto,
  • Sandra Ulrich Ngueveu

摘要

We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We prove that using absolute approximations of the players’ objective functions and then computing its Nash equilibria is equivalent to computing approximate Nash equilibria where the approximation factor is doubled. In practice, we propose an algorithm to approximate the players’ objective functions via piecewise linear approximations. The numerical experiments on a cybersecurity investment game combined with a detailed analysis of the results show the computational effectiveness of our approach.