Stochastic Variational Approach for Random Cournot-Nash Principle
Annamaria Barbagallo, Массимилиано Феррара, Paolo Mauro · 2021
In this note we study a stochastic variational inequality which models the Cournot-Nash equilibrium principle with uncertainty. Some existence results for the random equilibrium solutions are showed. Making use of the infinite dimensional Lagrange duality theory, the existence of Lagrange multipliers associated to the problem is obtained. Moreover, the behavior of control policies with uncertainty, whose aim is to regulate the exportation through the adjustment of taxes on firms, is investigated. In other words, the random policymaker optimization problem is analyzed by means of a stochastic inverse variational inequality. Finally, a numerical example is discussed.