Mean-field games of finite-fuel capacity expansion with singular controls
Mean-field games of finite-fuel capacity expansion with singular controls
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DOI：
10.1214/21-aap1771
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
L. Campi;T. Angelis;Maddalena Ghio;G. Livieri
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文献类型：
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作者：
L. Campi;T. Angelis;Maddalena Ghio;G. Livieri
我们研究纳什均衡的一系列对称$N$-玩家随机游戏的有限燃料容量扩张奇异控制和他们的平均场游戏（MFG）对应。我们构建了一个解决方案的MFG通过一个简单的迭代方案，产生一个最优控制的Skorokhod反射在（状态依赖）表面分裂的状态空间中的行动和不行动的区域。然后，我们表明，解决方案的MFG的容量扩张诱导近似纳什均衡的$N$玩家游戏的近似误差$\vareps $去为零的$N$趋于无穷大。我们的分析完全依赖于概率的方法，并扩展了著名的奇异随机控制和最优停止之间的连接到一个平均场框架。
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 in action and inaction region. 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.