Computing Approximate Nash Equilibria for Integer Programming Games - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes
Preprints, Working Papers, ... Year : 2024

Computing Approximate Nash Equilibria for Integer Programming Games

Abstract

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. Our numerical experiments on a cybersecurity investment game show the computational effectiveness of our approach.

Dates and versions

hal-04449901 , version 1 (09-02-2024)

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Aloïs Duguet, Margarida Carvalho, Gabriele Dragotto, Sandra Ulrich Ngueveu. Computing Approximate Nash Equilibria for Integer Programming Games. 2024. ⟨hal-04449901⟩
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