Densely Defined Equilibrium Problems

Szilárd László () and Adrian Viorel
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Szilárd László: Technical University of Cluj-Napoca
Adrian Viorel: Technical University of Cluj-Napoca

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 1, No 3, 52-75

Abstract: Abstract In the present work, we deal with set-valued equilibrium problems, for which we provide sufficient conditions for the existence of a solution. The conditions, that we consider, are imposed not on the whole domain, but rather on a self-segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu–Gale–Nikaïdo-type theorem, with a considerably weakened Walras law in its hypothesis. Furthermore, we consider a noncooperative $$n$$ n -person game and prove the existence of a Nash equilibrium, under assumptions that are less restrictive than the classical ones.

Keywords: Self-segment-dense set; Set-valued equilibrium problem; Debreu–Gale–Nikaïdo-type theorem; Nash equilibrium; 47H04; 47H05; 26B25; 26E25; 90C33 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-014-0702-8

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