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 Advanced results on variational inequality formulation in oligopolistic market equilibrium problem

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 935-947 ◽  
Author(s):  
Annamaria Barbagallo
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Lipschitz Continuity ◽  
Dynamic Equilibrium ◽  
Market Equilibrium ◽  
Equilibrium Solutions ◽  
Evolutionary Variational Inequality ◽  
Oligopolistic Market ◽  
Continuity Result ◽  
Discretization Procedure

The aim of the paper is to study the regularity of the solution to the evolutionary variational inequality governing the dynamic oligopolistic market equilibrium problem in presence of production excesses. More precisely, we obtain a Lipschitz continuity result with respect to time for such a solution. Moreover, we introduce a discretization procedure for computing dynamic equilibrium solutions and we provide a numerical example.

scholarly journals Time-Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses

2012 ◽  
Vol 2012 ◽  
pp. 1-35 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Paolo Mauro
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Variational Formulation ◽  
Market Equilibrium ◽  
Equilibrium Solutions ◽  
Equilibrium Conditions ◽  
Infinite Dimensional ◽  
Oligopolistic Market ◽  
Existence And Regularity Results ◽  
Regularity Results

The paper is concerned with the variational formulation of the oligopolistic market equilibrium problem in presence of both production and demand excesses. In particular, we generalize a previous model in which the authors, instead, considered only the problem with production excesses, by allowing also the presence of demand excesses. First we examine the equilibrium conditions in terms of the well-known dynamic Cournot-Nash principle. Next, the equilibrium conditions will be expressed in terms of Lagrange multipliers by means of the infinite dimensional duality theory. Then, we show the equivalence between the two conditions that are both expressed by an appropriate evolutionary variational inequality. Moreover, thanks to the variational formulation, some existence and regularity results for equilibrium solutions are proved. At last, a numerical example, which illustrates the features of the problem, is provided.

Duality theory for the dynamic oligopolistic market equilibrium problem

Optimization ◽  
2011 ◽  
Vol 60 (1-2) ◽  
pp. 29-52 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Antonino Maugeri
Keyword(s):  
Equilibrium Problem ◽  
Duality Theory ◽  
Market Equilibrium ◽  
Oligopolistic Market

A PROGRESSIVE EQUILIBRATION ALGORITHM FOR GENERAL MARKET EQUILIBRIUM PROBLEMS UNDER CONSTRAINTS

2013 ◽  
Vol 30 (03) ◽  
pp. 1340006
Author(s):  
GANG QIAN ◽  
HONGJIN HE ◽  
DEREN HAN
Keyword(s):  
Variational Inequality ◽  
Global Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Market Equilibrium ◽  
Numerical Results ◽  
Price Equilibrium ◽  
Spatial Price Equilibrium ◽  
Scarce Resources ◽  
Spatial Price

This paper considers the general Spatial Price Equilibrium (SPE) problem under constraints of supply-guarantee at demand markets and, in the meantime, protecting the scarce resources at supply markets. We first formulate the equilibrium problem as a variational inequality (VI) problem with partially unknown mapping. Then, we propose a progressive equilibration algorithm for solving the problem under consideration. The global convergence of the proposed method is proved under suitable assumptions. Some preliminary numerical results demonstrate the reliability of the proposed algorithm.

Dynamic Oligopolistic Market Equilibrium Problems with Production Excesses: A Variational Approach

2011 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Paolo Mauro ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Variational Approach ◽  
Equilibrium Problems ◽  
Market Equilibrium ◽  
Oligopolistic Market

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.

Sign in / Sign up

Export Citation Format

Share Document