Existence of quasi-equilibria on unbounded constraint sets

Cotrina, John; Hantoute, Abderrahim; Svensson, Anton

doi:10.1080/02331934.2020.1778690

Cited by 11 publications

(10 citation statements)

References 23 publications

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“…Most of the results concerning (QEP) are stated in a finite-dimensional framework, on a compact set C, and they involve generalized monotonicity assumptions on f together with upper semicontinuity of the set-valued map which describes the constraint, as well as lower semicontinuity of this map with the additional assumption of the closedness of the set of fixed points (see, for instance, [9]). In case of an unbounded set C, an additional coercivity condition is required (for a recent result, see [12]).…”

Section: Introductionmentioning

confidence: 99%

Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

2021

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In this paper we investigate quasi equilibrium problems in a real Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered.

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Section: Introductionmentioning

confidence: 99%

Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

2021

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“…A special case of this concept is used in [26] under the name "Pareto equilibrium" for a bicriteria game with C i = −R 2 + . A generalized Nash equilibrium studied in [9] (resp. [10]) corresponds to our concept where Y i = R, C i = R + (resp.…”

Section: Furthermore For Allmentioning

confidence: 99%

Existence of solutions of a generalized bifunction-set optimization problem

Tuấn

Sách

2023

JIMO

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<p style='text-indent:20px;'>An existence result is established for a generalized bifunction-set optimization problem, under some verifiable assumptions. Its proof is based on a Browder fixed point theorem and the KKMFan-Lemma. As applications of the main result of this paper, we obtain new existence results for some generalized versions of Kuroiwa set optimization problems and strong vector quasiequilibrium problems. Examples are provided. One of them is a non-cooperative generalized game with utility multifunctions.</p>

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“…Existence of equilibria for Nash games has been well-studied and the appropriate framework seems to be the case of (generalized) convexity conditions (see e.g. [7,6]). However, for our purpose of considering the Nash game between the leaders of a bilevel game, generalized convexity conditions are generally not satisfied, and moreover, equilibria may fail to exist (See [30,Example 4]).…”

Section: Preliminaries and Notationmentioning

confidence: 99%

Existence of solutions for deterministic bilevel games under a general Bayesian approach

Salas¹,

Svensson²

2020

Preprint

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We propose a novel approach for bilevel games, called the stochastic approach, which solves the ambiguity that arises when optimal responses of followers are not unique. This model provides a spectrum of alternatives between the classic optimistic and pessimistic approaches. We model how leaders anticipate the followers' reaction as decision-dependent probability distributions, which we call beliefs. Several existence results are provided for this new approach, particularly for bilevel games with a single follower.

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Existence of quasi-equilibria on unbounded constraint sets

Cited by 11 publications

References 23 publications

Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

Existence of solutions of a generalized bifunction-set optimization problem

Existence of solutions for deterministic bilevel games under a general Bayesian approach

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