A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets

• Published in: Mathematical finance 2022-07, Vol.32 (3), p.779-824
• Main Authors: Shrivats, Arvind V., Firoozi, Dena, Jaimungal, Sebastian
• Format: Article
• Language: English
• Subjects: Alternative energy sources; cap and trade; commodity markets; Differential equations; Equilibrium; equilibrium pricing; Game theory; Games; Lower bounds; Markets; McKean–Vlasov; mean‐field games; Noncompliance; Optimization; Renewable energy; Renewable resources; Simulation; Solar energy; SREC; Trading; Uncertainty; Uniqueness; variational analysis
• ISSN: 0960-1627; 1467-9965
• DOI: 10.1111/mafi.12345

Solar renewable energy certificate (SREC) markets are a market‐based system that incentivizes solar energy generation. A regulatory body overseeing load serving entities imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a tradeable certificate for each MWh generated. Firms seek to navigate the market optimally by modulating their SREC generation and trading rates. As such, the SREC market can be viewed as a stochastic game, where agents interact through the SREC price. We study this stochastic game by solving the mean‐field game (MFG) limit with subpopulations of heterogeneous agents. Market participants optimize costs accounting for trading frictions, cost of generation, nonlinear noncompliance costs, and generation uncertainty. Moreover, we endogenize SREC price through market clearing. We characterize firms' optimal controls as the solution of McKean–Vlasov (MV) forward‐backward stochastic differential equations (FBSDEs) and determine the equilibrium SREC price. We establish the existence and uniqueness of a solution to this MV‐FBSDE, and prove that the MFG strategies form an ε$\epsilon$‐Nash equilibrium for the finite player game. Finally, we develop a numerical scheme for solving the MV‐FBSDEs and conduct a simulation study.