We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem. Using the framework of relaxed optimal stopping allows us to prove the existence of a relaxed Nash equilibrium and the uniqueness of the associated value of the representative agent under mild assumptions.
As an example of the application of the developed theory, we consider a model of the electricity market. In our model, there are two types of agents: the renewable producers and the conventional producers. The renewable producers choose the optimal moment to build new renewable plants, and the conventional producers choose the optimal moment to exit the market. The agents interact through the market price, determined by matching the aggregate supply of the two types of producers with an exogenous demand function.
An empirical example, inspired by the UK electricity market is presented. The example shows that while renewable subsidies may entail a cost to the consumer in terms of higher peakload prices. In order to avoid rising prices, the renewable subsidies must be combined with mechanisms ensuring that sufficient conventional capacity remains in place to meet the energy demand during peak periods.