Regulation of pollution in a Cournot equilibrium

Abstract

In the traditional Cournot model producers influence each other’s decisions through revenue earned in the product market. Rosen (1965) introduced the notion of a coupled constraints equilibrium which allowed players to affect their rivals’ strategy space as well. Krawczyk (2005) applied this idea to the regulation of environmental pollution where a cap on aggregate emissions implies a constraint across firms’ activity levels. He solved the model with a diagonalization algorithm obtaining linear convergence. We formulate this problem as a complementarity problem and apply a Newton algorithm obtaining a quadratic convergence. We show that the conditions under which this model has a unique solution and the algorithm computes the solution are analogous to those for the traditional Cournot model.