H. Cao, X. Guo, “MFGs for partially reversible investment”. Stochastic Processes and their Applications, 150, 995-1014.
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 ε-Nash Equilibrium to the corresponding N-player game, with ε= O 1 N.