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Cyclically monotone equilibrium problems and Ekeland’s principle

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  • Massimiliano Giuli

    (Computer Science and Mathematics)

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.

Suggested Citation

  • Massimiliano Giuli, 2017. "Cyclically monotone equilibrium problems and Ekeland’s principle," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 231-242, November.
    • Handle: RePEc:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0188-6
    DOI: 10.1007/s10203-017-0188-6
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    References listed on IDEAS

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    1. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    2. M. Castellani & M. Giuli, 2013. "Refinements of existence results for relaxed quasimonotone equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1213-1227, December.
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    Cited by:

    1. John Cotrina & Michel Théra & Javier Zúñiga, 2020. "An Existence Result for Quasi-equilibrium Problems via Ekeland’s Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 336-355, November.

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    More about this item

    Keywords

    Equilibrium problem; Ekeland’s variational principle; Minty’s lemma;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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