A Stackelberg Mean Field Game for Green Regulator with a Large Number of Prosumers

We model a Stackelberg game in a power market with rational consumers and a benevolent regulator as a meanfield game. The Stackelberg leader, who is a government regulator, sets the grid distribution fees so as to maximize the total welfare of the consumers, while also ensuring the solvency of the electricity producers and while satisfying renewable production targets. The Stackelberg followers, who are rational prosumers of electricity, maximize their personal utilities by choosing their individual Photovoltaics investments that provides an alternative to buying electricity from the grid, and hence can also produce electricity. With the representative prosumer's demand evolving as an Ornstein-Uhlenbeck process, we find a closed form mean-field game approximation to prosumer's optimal strategy, and use that to calculate the optimal fees set by the regulator. Using these we numerically investigate and explain the influence of various market conditions on the optimal distribution fees.