MFGs for partially reversible investment

TL;DR

This paper develops explicit solutions for mean-field games related to partially reversible investments, analyzing how model parameters influence strategies and equilibrium prices, and establishing their approximation to finite-player games.

Contribution

It provides an explicit MFG solution for partially reversible investment problems and demonstrates its approximation accuracy for finite-player games.

Findings

Model parameters influence equilibrium prices.

The MFG solution approximates the N-player game with error O(1/√N).

Sensitivity analysis compares MFG and single-agent control solutions.

Abstract

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis to compare the solution for the MFG with that for the single-agent control problem. It shows that in the MFG, model parameters not only affect the optimal strategies as in the single-agent case, but also influence the equilibrium price. It then establishes that the solution to the MFG is an $\epsilon$-Nash Equilibrium to the corresponding $N$-player game, with $\epsilon=O\left(\frac{1}{\sqrt N}\right)$.