A Mean Field Game approach for pollution regulation of competitive firms

We develop a model based on mean-field games of competitive firms that produce products via the so-called AK production function and generate pollution as a byproduct.    We analyze a popular type of pollution regulation: cap-and-trade. Firms can respond to regulation by combining pollution abatement, output reduction, and emission trading; a regulator dynamically allocates emission allowances to each firm. Many firms $1 \leq I \leq N$ interact through their linear inverse demand curve. The resulting mean-field game is of linear quadratic type, equivalent to a mean-field type control problem. We find explicit solutions to this problem where the coefficient functions are given as the solutions to differential equations of Riccati type. We study the carbon emission equilibrium price that satisfies the so-called market clearing condition, finding a particular form of FBSDE of McKean-Vlasov type with common noise; the solution to this equation provides an approximate equilibrium price. In addition, the solution to the mean-field limit problem provides asymptotic market clearing in the large $N$ limit. Finally, we show that the degree of competition is critical in determining the economic consequences of pollution regulation.  

 

Joint work with: Gianmarco Del Sarto and Marta Leocata.