This paper analyzes a class of MFGs with singular controls motivated from the partially reversible problem. It establishes the existence of the solution when controls are of bounded velocity, solves explicitly the game when controls are of finite variation, and presents sensitivity analysis to compare the single-player game with the MFG . Our analysis shows that MFGs, when appropriately formulated, can demonstrate genuine gameeffects even without heterogeneity among players and additional common noise\left({\sqrt N}}\right) .
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) .
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MFGs
infinite-time-horizon stochastic games
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establishes the existence of the solution when controls are of bounded velocity, solves explicitly the game when controls are of finite variation,
provides an explicit solution for the mean-field game (MFG)
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single-player game with the MFG . Our analysis shows that MFGs, when appropriately formulated, can demonstrate genuine gameeffects even without heterogeneity among players and additional common noise
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
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