scholarly journals Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
I. Benedetti ◽  
M. B. Donato ◽  
M. Milasi
Keyword(s):  
Variational Inequality ◽  
Equilibrium Model ◽  
Variational Approach ◽  
Existence Result ◽  
Competitive Equilibrium ◽  
Quasivariational Inequalities ◽  
Existence Of Equilibrium ◽  
Upper Semicontinuous ◽  
Generalized Quasivariational Inequalities ◽  
Quasi Variational Inequality

A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach.

scholarly journals A generalised quasi-variational inequality without upper semicontinuity

1996 ◽  
Vol 54 (2) ◽  
pp. 247-254 ◽  
Author(s):  
Paolo Cubiotti ◽  
Xian-Zhi Yuan
Keyword(s):  
Variational Inequality ◽  
Convex Subset ◽  
Existence Result ◽  
Upper Semicontinuity ◽  
Nonempty Closed Convex Subset ◽  
Positive Answer ◽  
Upper Semicontinuous ◽  
Quasi Variational Inequality ◽  
General Existence ◽  
Image Position

In this note we deal with the following problem: given a nonempty closed convex subset X of Rn and two multifunctions Γ : X → 2X and , to find ( such thatWe prove a very general existence result where neither Γ nor Φ are assumed to be upper semicontinuous. In particular, our result give a positive answer to an open problem raised by the first author recently.

scholarly journals Existence of General Competitive Equilibria: A Variational Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
G. Anello ◽  
F. Rania
Keyword(s):  
Variational Inequalities ◽  
Finite Number ◽  
Variational Methods ◽  
Variational Approach ◽  
Existence Result ◽  
Competitive Equilibrium ◽  
Utility Functions ◽  
Locally Lipschitz ◽  
Competitive Equilibria

We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities.

Existence and stability for a generalized differential mixed quasi-variational inequality

2018 ◽  
Vol 34 (3) ◽  
pp. 347-354
Author(s):  
WEI LI ◽  
◽  
YI-BIN XIAO ◽  
XING WANG ◽  
JUN FENG ◽  
...  
Keyword(s):  
Weak Solution ◽  
Variational Inequality ◽  
Existence Result ◽  
Upper Semicontinuity ◽  
Measurable Selection ◽  
Existence And Stability ◽  
Quasi Variational Inequality ◽  
Carathéodory Weak Solution ◽  
Generalized Differential ◽  
Stability Results

In the present paper, we investigate a generalized differential mixed quasi-variational inequality consisting of a system of an ordinary differential equation and a generalized mixed quasi-variational inequality. By using an important result concerning the measurable selection, we prove the existence of Caratheodory weak solution to ´ the generalized differential mixed quasi-variational inequality. Then, with the existence result, we establish two stability results for the generalized differential mixed quasi-variational inequality under different conditions, i.e., upper semicontinuity and lower semicontinuity of the Caratheodory weak solution with respect to the ´ parameter, which is a perturbation of some mappings in the generalized mixed quasi-variational inequality.

scholarly journals A Quasi-Variational Approach for the Dynamic Oligopolistic Market Equilibrium Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Paolo Mauro
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Production Function ◽  
Variational Approach ◽  
Equilibrium Distribution ◽  
Market Equilibrium ◽  
Capacity Constraints ◽  
Realistic Case ◽  
Oligopolistic Market ◽  
Quasi Variational Inequality

The paper is concerned with the dynamic oligopolistic market equilibrium problem in the realistic case in which we allow the presence of capacity constraints and production excesses and, moreover, we assume that the production function depends not only on the time but also on the equilibrium distribution. As a consequence, we introduce the generalized dynamic Cournot-Nash principle in the elastic case and prove the equivalence between this equilibrium definition and a suitable evolutionary quasi-variational inequality. For completeness we make the analysis of existence, regularity, and sensitivity of the solution. In the end, a numerical example is provided.

scholarly journals Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces

2020 ◽  
Vol 10 (1) ◽  
pp. 276-282
Author(s):  
Robert V. Namm ◽  
Georgiy I. Tsoy
Keyword(s):  
Variational Inequality ◽  
Elastic Body ◽  
Approximation Method ◽  
Coulomb Friction ◽  
Auxiliary Problem ◽  
Crack Problem ◽  
Successive Approximation Method ◽  
Elastic Crack ◽  
Quasi Variational Inequality ◽  
Crack Faces

AbstractWe consider an equilibrium problem for an elastic body with a crack, on the faces of which unilateral non-penetration conditions and Coulomb friction are realized. This problem can be formulated as quasi-variational inequality. To solve it, the successive approximation method is applied. On each outer step of this method, we solve an auxiliary problem with given friction. We solve the auxiliary problem by using modified Lagrange functionals. Numerical results are presented.

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