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Approximate Nash Equilibria in Large Nonconvex Aggregative Games

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kang Liu & Nadia Oudjane & Cheng Wan, 2023. "Approximate Nash Equilibria in Large Nonconvex Aggregative Games," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1791-1809, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1791-1809
    DOI: 10.1287/moor.2022.1321
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