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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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Gamma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u0393<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-convergence notion for equilibrium problems is introduced and discussed as well as applied to a class of penalized generalized Nash equilibrium problems and quasi-variational inequalities. 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