A Mean Field Game Model for Renewable Investment Under Long-Term Uncertainty and Risk Aversion

We consider a stylized model for investment into renewable power plants under long-term uncertainty. We model risk-averse agents facing heterogeneous weather conditions and a common noise including uncertainty on demand trends, future fuel prices and the average national weather conditions. The objective of each agent is to maximize multistage profit by controlling investment in discrete time steps. We analyze this model in a noncooperative game setting with N players, where the interaction among agents occurs through the spot price mechanism. Our model extends to a mean field game with common noise when the number of agents is infinite. We prove that the N-player game admits a Nash equilibrium. Moreover, we prove that under appropriate assumptions, any sequence of Nash equilibria to the N-player game converges to the unique solution of the MFG game. Our numerical experiments highlight the impact of the risk aversion parameter and the importance of correctly specifying the distribution of the heterogeneity among agents. Moreover, we demonstrate that the results obtained by our model cannot be replicated by a model based on a representative agent with a unique parameter that would represent homogenized weather conditions. This emphasizes the importance of including explicit modeling of heterogeneity in prospective models when a heterogeneous parameter is expected to have a significant influence on the outcomes.