A Mean Field Game for Capacity Expansion Modeling

TL;DR

This paper models the strategic investment decisions of renewable electricity producers using a mean field game framework, capturing crowding effects and analyzing equilibrium dynamics under various market conditions.

Contribution

It introduces a mean field game model for capacity expansion, incorporating heterogeneity and crowding effects, with analytical and numerical solutions for equilibrium analysis.

Findings

Investment responds to market conditions and shocks

Crowding effects influence capacity growth

Analytical solutions in tractable cases

Abstract

This paper studies the optimal investment behavior of renewable electricity producers in a competitive market, where both prices and installation costs are influenced by aggregate industry activity. We model the resulting crowding effects using a mean field game framework, capturing the strategic interactions among a continuum of heterogeneous producers. The equilibrium dynamics are characterized via a coupled system of Hamilton-Jacobi-Bellman and Fokker-Planck equations, which describe the value function of a representative producer and the evolution of the distribution of installed capacities over time. We analyze both deterministic and stochastic versions of the model, providing analytical insights in tractable cases and developing numerical methods to approximate the general solution. Simulation results illustrate how aggregate investment responds to changing market conditions, cost structures, and exogenous productivity shocks.