This was part of Applications of Mean Field Games

Equilibrium Pricing in Renewable Energy Certificate (REC) Markets using Mean Field Game Methodology

Dena Firoozi, HEC Montreal

Wednesday, November 17, 2021

Abstract: In a renewable energy certificate (REC) market a regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via renewable means, providing them with a certificate for each MWh generated. Regulated firms seek to navigate the market to minimize the cost imposed on them, by modulating their REC generation and trading activities. As such, the REC market can be viewed through the lens of a large stochastic game with heterogeneous agents, where agents interact through the market price of the certificates. We study this stochastic game by solving the mean-field game (MFG) limit with sub-populations of heterogeneous agents. Moreover, we endogenize REC prices through market clearing. Using techniques from variational analysis, we characterize firms’ optimal controls as the solution of McKean-Vlasov (MV) FBSDEs and determine the equilibrium REC price. We establish the existence and uniqueness of a solution to this MV-FBSDE, and further prove that the MFG strategies have the Epsilon-Nash property for the finite player game. Finally, we develop a numerical scheme for solving the MV-FBSDEs and conclude by demonstrating how firms behave in equilibrium using simulated examples.