WIAS Preprint No. 2879, (2021)

A generalized $Gamma$-convergence concept for a type of equilibrium problems


  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Stengl, Steven-Marian

2020 Mathematics Subject Classification

  • 91B50 91A11 91A80 35Q91 49J40 47J20 35A15


  • Equilibrium problems, Nash games, quasi-variational inequalities, Γ-convergence, penalty methods




A novel generalization of Γ-convergence applicable to a class of equilibrium problems is studied. After the introduction of the latter, a variety of its applications is discussed. The existence of equilibria with emphasis on Nash equilibrium problems is investigated. Subsequently, our Γ-convergence notion for equilibrium problems, generalizing the existing one from optimization, is introduced and discussed. The work ends with its application to a class of penalized generalized Nash equilibrium problems and quasi-variational inequalities.

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