Time-Dependent Generalized Nash Equilibrium Problem

Cotrina, John; Zúñiga, Javier

doi:10.1007/s10957-018-1383-5

Cited by 7 publications

(5 citation statements)

References 17 publications

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“…We obtain ǫ > 0 satisfying B(x i , ǫ) ∩ C L ⊆ H, since we have following relation due to (15), Assume that 0 < λ < ǫ ||y ′ i −xi|| L 2 , then y • i = λy ′ i + (1 − λ)x i ∈ Ki (p). Thus, by (19) we obtain x * i , y ′ i − xi m ≥ 0 which contradicts our hypothesis in (22).…”

Section: Application To Dynamic Competitive Equilibrium Problemmentioning

confidence: 99%

“…We will employ the existence theorems proved in Section 3 to show the occurrence of dynamic competitive equilibrium for time-dependent pure exchange economy defined over the time interval [0, T ], T > 0 (one may refer [1,15,17,18] for more information). For this purpose, we first characterize the dynamic competitive equilibrium problem as a QVI which is a specific case of the general problem QVI(F, f, K) (2).…”

Section: Application To Dynamic Competitive Equilibrium Problemmentioning

confidence: 99%

“…We assert that the vector x, which solves QVI (17), also fulfills (15). By using (20) In the above inequality, suppose p = (p k ) k∈J ∈ P is considered as p j = 1 for some j and p k = 0 if k = j.…”

Section: Application To Dynamic Competitive Equilibrium Problemmentioning

confidence: 99%

“…In fact, one can verify that M i is l.s.c. over D if the below-stated survivability condition holds for each j ∈ J (see [1,Lemma 3.4]), [1,15,16]).…”

Section: Remark 41 (A)mentioning

confidence: 99%

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Existence Theorems on Quasi-variational Inequalities over Banach Spaces and its Applications to Time-dependent Pure Exchange Economy

Sultana¹,

Valecha²

2023

Preprint

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We study a class of quasi-variational inequality problems defined over infinite dimensional Banach space and deduce sufficient conditions for ensuring solutions to such problems under the upper semi-continuity and pseudomonotonicity assumptions on the map defining the inequalities. The special structure of the quasi-variational inequality enables us to show the occurrence of solutions for such inequalities based on the classical existence theorem for variational inequalities. This special type of quasi-variational inequalities is motivated by the pure exchange economic problems and Radner equilibrium problems for sequential trading game. Further, we study the solvability of the specific class of quasi-variational inequalities on Banach spaces in which the constraint map may admit unbounded values. Finally, we demonstrate the occurrence of dynamic competitive equilibrium for a time-dependent pure exchange economy as an application.

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Section: Application To Dynamic Competitive Equilibrium Problemmentioning

confidence: 99%

Section: Application To Dynamic Competitive Equilibrium Problemmentioning

confidence: 99%

Section: Application To Dynamic Competitive Equilibrium Problemmentioning

confidence: 99%

“…In fact, one can verify that M i is l.s.c. over D if the below-stated survivability condition holds for each j ∈ J (see [1,Lemma 3.4]), [1,15,16]).…”

Section: Remark 41 (A)mentioning

confidence: 99%

See 2 more Smart Citations

Existence Theorems on Quasi-variational Inequalities over Banach Spaces and its Applications to Time-dependent Pure Exchange Economy

Sultana¹,

Valecha²

2023

Preprint

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“…sistemas de engenharia, comportamentais e financeiros tornam este tópico de pesquisa uma ferramenta extremamente importante com uma ampla gama de aplicações (Han et al, 2019;Başar and Zaccour, 2018). De fato, podemos encontrar numerosos resultados para teoria e prática na literatura correspondente a jogos diferenciais (Wang et al, 2018;Cotrina and Zúñiga, 2018;Aussel and Svensson, 2019;Alasseur et al, 2020).…”

Section: Introductionunclassified

Busca do Equilíbrio de Nash em Jogos Não-cooperativos com Atrasos

Oliveira

Rodrigues

Krstić

et al. 2020

Anais Do Congresso Brasileiro De Automática 2020

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Neste artigo, propomos uma estratégia de Busca pelo Equilíbrio de Nash baseada no não-conhecimento do modelo que garanta ao sistema de malha fechada convergência local com propriedades de estabilidade em jogos quadrático não-cooperativos, do tipo duopólio, com ações arbitrariamente atrasadas. Em nosso cenário não-cooperativo, os jogadores têm acesso apenas aos seus próprios lucros. Para compensar atrasos distintos nas entradas dos dois jogadores, emprega-se a busca extremal por controle de fronteira via realimentação por predição com estimativas baseadas na média. Aplica-se uma análise de pequenos ganhos para a malha formada por equações diferencias ordinárias (EDO) - equações diferencias parciais (EDP), bem como a teoria da média em dimensões infinitas, devido ao estado dimensional infinito dos atrasos temporais, a fim de obter resultados de convergência local a uma pequena vizinhança do Equilíbrio de Nash. Quantifica-se o tamanho desse conjunto residual e os resultados teóricos validados através de um exemplo de simulação.

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Quasi-equilibrium problems with non-self constraint map

Cotrina

Zúñiga

2019

J Glob Optim

Self Cite

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In 2016 Aussel, Sultana and Vetrivel developed the concept of projected solution for quasi-variational inequality problems and projected Nash equilibrium. We introduce a new concept of solution for quasi-equilibrium problems and we study the existence of such solutions. Additionally, as a consequence of our results, we give existence results of projected solutions for quasi-optimization problems, quasi-variational inequalities problems and generalized Nash equilibrium problems.

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Time-Dependent Generalized Nash Equilibrium Problem

Abstract: We prove an existence result for the time-dependent generalized Nash equilibrium problem under generalized convexity using a fixed point theorem. Furthermore, an application to the dynamic abstract economy is considered.

Cited by 7 publications

References 17 publications

Existence Theorems on Quasi-variational Inequalities over Banach Spaces and its Applications to Time-dependent Pure Exchange Economy

Existence Theorems on Quasi-variational Inequalities over Banach Spaces and its Applications to Time-dependent Pure Exchange Economy

Busca do Equilíbrio de Nash em Jogos Não-cooperativos com Atrasos

Quasi-equilibrium problems with non-self constraint map

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