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Journal Articles Mathematics of Operations Research Year : 2022

Approximate Nash equilibria in large nonconvex aggregative games

Abstract

This paper shows the existence of $\mathcal{O}(\frac{1}{n^\gamma})$-Nash equilibria in $n$-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players' actions, are lower semicontinuous in the former while $\gamma$-H\"{o}lder continuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of sum-aggregative games, which includes congestion games with $\gamma$ equal to 1, a gradient-proximal algorithm is used to construct $\mathcal{O}(\frac{1}{n})$-Nash equilibria with at most $\mathcal{O}(n^3)$ iterations. These results are applied to a numerical example concerning the demand-side management of an electricity system. The asymptotic performance of the algorithm when $n$ tends to infinity is illustrated.
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Dates and versions

hal-03023122 , version 1 (25-11-2020)
hal-03023122 , version 2 (08-10-2021)
hal-03023122 , version 3 (26-09-2022)

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Kang Liu, Nadia Oudjane, Cheng Wan. Approximate Nash equilibria in large nonconvex aggregative games. Mathematics of Operations Research, 2022, ⟨10.1287/moor.2022.1321⟩. ⟨hal-03023122v3⟩
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