Approximate Nash Equilibria in Large Nonconvex Aggregative Games

Kang Liu (), Nadia Oudjane () and Cheng Wan ()
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Kang Liu: Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France; Inria Saclay Center, 91120 Palaiseau, France
Nadia Oudjane: Research & Development, EDF Lab Paris-Saclay, 91120 Palaiseau, France; Finance for Energy Market Research Centre, France
Cheng Wan: Research & Development, EDF Lab Paris-Saclay, 91120 Palaiseau, France; Finance for Energy Market Research Centre, France

Mathematics of Operations Research, 2023, vol. 48, issue 3, 1791-1809

Abstract: This paper shows the existence of O ( 1 / n γ ) -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, whereas γ -Hölder 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 γ equal to one, a gradient-proximal algorithm is used to construct O ( 1 / n ) -Nash equilibria with at most 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.

Keywords: Primary: 91A06; secondary: 90C26; Shapley–Folkman lemma; sum-aggregative games; nonconvex game; large finite game; ϵ -Nash equilibrium; gradient-proximal algorithm; congestion game (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:3:p:1791-1809

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