Existence of Projected Solutions for Generalized Nash Equilibrium Problems

Bueno, Orestes; Cotrina, John

doi:10.1007/s10957-021-01941-9

Cited by 9 publications

(5 citation statements)

References 24 publications

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“…(XXVIII) In 2020, Park [30] generalizes his 1991 theorem [23] (XXIX) Bueno and Cortina [3] in 2021: We study the existence of projected solutions for generalized Nash equilibrium problems dened in Banach spaces, under mild convexity assumptions for each loss function and without lower semicontinuity assumptions on the constraint maps. Our approach is based on Himmelberg's xed point theorem.…”

Section: Further Sources Of Equivalents Of the Brouwer Theoremmentioning

confidence: 99%

Some new equivalents of the Brouwer fixed point theorem

PARK

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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This is to recollect the equivalent formulations of the Brouwer xed point theorem. We collect a large number of recently known sources of such equivalents. More recently, Jinlu Li obtained two xed point theorems on newly dened quasi-point-separable topological vector spaces. His theorems extend the Tychono xed point theorem on locally convex t.v.s. However, we note that his new theorems are logically equivalent to the Brouwer xed point theorem. Consequently, we add up our large list of such equivalents.

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Section: Further Sources Of Equivalents Of the Brouwer Theoremmentioning

confidence: 99%

Some new equivalents of the Brouwer fixed point theorem

PARK

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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“…For this reason, in [4] the authors introduced the more general notion of projected solutions of a quasi variational inequalities in finite dimension and later in [11] the case of quasi equilibrium problem was addressed. Due to possible more realistic applications, recently there has been an increasing interest in studying existence of projected solutions in more general settings (see, for instance, [1] and [8] ).…”

Section: Introductionmentioning

confidence: 99%

On Projected Solutions for Quasi Equilibrium Problems with Non-self Constraint Map

Bianchi¹,

Miglierina²,

Ramazannejad³

2023

Preprint

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In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative scheme which gives rise to a sequence weakly converging to a projected solution. Finally, as a particular case, we discuss the existence of projected solutions to a quasi variational inequality problem.

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“…Quasi-variational inequality problems have been proven an efficient tool to study the GNEPs. Very recently, Bueno and Cotrina [10] studied the projected solutions of GNEP with the help of quasi-variational inequality problems. For more recent relevant works, we refer to [11,12] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Split modeling approach to non-cooperative strategic games

2023

Appl. Set-Valued Anal. Optim.

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In this paper, we examine how can one achieve equilibrium when two related non-cooperative strategic games are being played. We propose a split generalized Nash equilibrium problem for two non-cooperative strategic games and also define an equivalent split quasi-variational inequality problem. Further, by using the techniques of proving existence of quasi-variational inequality problems, we establish the existence of equilibria. Moreover, as an application, we investigate our split generalized Nash equilibrium problem in the terms of river basin pollution problem.

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Existence of Projected Solutions for Generalized Nash Equilibrium Problems

Cited by 9 publications

References 24 publications

Some new equivalents of the Brouwer fixed point theorem

Some new equivalents of the Brouwer fixed point theorem

On Projected Solutions for Quasi Equilibrium Problems with Non-self Constraint Map

Split modeling approach to non-cooperative strategic games

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