MFGs for partially reversible investment

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 $ε$-Nash Equilibrium to the corresponding $N$-player game, with $ε=O\left(\frac{1}{\sqrt N}\right)$.

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