Cyclically monotone equilibrium problems and Ekeland’s principle

Massimiliano Giuli ()
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Massimiliano Giuli: Computer Science and Mathematics

Decisions in Economics and Finance, 2017, vol. 40, issue 1, No 12, 242 pages

Abstract: Abstract We study the existence of equilibria and approximate equilibria avoiding any assumption of convexity both for the domain and for the bifunction. Our approach is based on the concept of cyclic monotonicity for bifunctions. First, we exploit this notion to obtain an Ekeland’s variational principle for bifunctions which leads to the existence of approximate solutions of the so-called Minty equilibrium problem. Then, we prove the existence of equilibria in compact and noncompact settings. We introduce a new notion as a key tool for deriving a Minty’s lemma avoiding the use of convexity.

Keywords: Equilibrium problem; Ekeland’s variational principle; Minty’s lemma (search for similar items in EconPapers)
JEL-codes: C02 C61 C62 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10203-017-0188-6

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