Axioms
(Jul 2023)
A Discrete Characterization of the Solvability of Equilibrium Problems and Its Application to Game Theory
Maria Isabel Berenguer,
Domingo Gámez,
Ana Isabel Garralda-Guillem,
Manuel Ruiz Galán
Affiliations
Maria Isabel Berenguer
E.T.S. Ingeniería de Edificación, Department of Applied Mathematics, Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
Domingo Gámez
E.T.S. Ingeniería de Edificación, Department of Applied Mathematics, Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
Ana Isabel Garralda-Guillem
E.T.S. Ingeniería de Edificación, Department of Applied Mathematics, Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
Manuel Ruiz Galán
E.T.S. Ingeniería de Edificación, Department of Applied Mathematics, Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
DOI
https://doi.org/10.3390/axioms12070666
Journal volume & issue
Vol. 12,
no. 7
Abstract
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We state a characterization of the existence of equilibrium in terms of certain finite subsets under compactness and transfer upper semicontinuity conditions. In order to derive some consequences on game theory—Nash equilibrium and minimax inequalities—we introduce a weak convexity concept.
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