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 $\epsilon=O\left(\frac{1}{\sqrt N}\right)$.

中文翻译：

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用于部分可逆投资的 MFG

本文分析了一类由部分可逆问题驱动的具有奇异控制的无限时间范围随机博弈。它为平均场博弈 (MFG) 提供了明确的解决方案，并提供了敏感性分析，以将 MFG 的解决方案与单代理控制问题的解决方案进行比较。结果表明，在MFG中，模型参数不仅影响单代理情况下的最优策略，而且影响均衡价格。然后确定 MFG 的解决方案是对应的 $N$ 玩家博弈的 $\epsilon$-纳什均衡，其中 $\epsilon=O\left(\frac{1}{\sqrt N}\right) $.