General stochastic variational formulation for the oligopolistic market equilibrium problem with excesses

2017 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Guglielmo Di Meglio ◽  
Paolo Mauro
Keyword(s):  
Equilibrium Problem ◽  
Variational Formulation ◽  
Market Equilibrium ◽  
Oligopolistic Market ◽  
General Stochastic

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.

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.

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

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.

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