论文标题
具有奇异控制的有限燃油能力扩展的平均场景
Mean-Field Games of Finite-Fuel Capacity Expansion with Singular Controls
论文作者
论文摘要
我们研究了NASH Equilibria，其中包括一系列对称$ n $ n $玩家的随机游戏，其中有限燃油能力扩展，并具有单数控制及其平均场地游戏（MFG）对手。我们通过简单的迭代方案构建MFG的解决方案，该方案在（状态依赖性的）表面上以Skorokhod反射产生最佳控制，该方案将状态空间拆分为行动和无行为区域。然后，我们证明，麦克风扩展的解决方案会导致$ n $ - 玩家游戏的近似Nash Equilibria，近似错误$ \ VAREPSILON $将零作为$ n $趋于无限。我们的分析完全依赖于概率方法，并扩展了奇异随机控制和最佳停止之间的众所周知的联系。
We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface that splits the state space into action and inaction regions. We then show that a solution of the MFG of capacity expansion induces approximate Nash equilibria for the $N$-player games with approximation error $\varepsilon$ going to zero as $N$ tends to infinity. Our analysis relies entirely on probabilistic methods and extends the well-known connection between singular stochastic control and optimal stopping to a mean-field framework.
