Stability of time-dependent elastic Nash equilibrium in oligopolistic markets under perturbation

In this paper, we consider time-dependent elastic Nash equilibria in oligopolistic markets.Our analysis underlines the perturbation phenomena that should be taken into account in the study of such equilibrium problems.Precisely, there are both internal and external sources generating variations at any time of the commodity shipment between the supply market and the demand market.This also affects, in principle, commodity outputs as well as the commodity at demand markets.Accordingly, the three costs of production, the storage and the transportation, respectively, involved in a such model are perturbed by the same and/or another perturbation.Then, in this work, we first fix the parametric market equilibrium model for our problem, which we characterize by a time-dependent quasi-variational inequality problem what enables us to state and prove our main result on the stability of the parametric equilibrium commodity shipment in question.Our key tools make recourse to recent developments of quasi-equilibrium problems as well as the qualitative stability of fixed points of set-valued maps.