Stationary Discounted and Ergodic Mean Field Games with Singular Controls
研究了代表性玩家通过折扣和遍历绩效标准与人口长期加权平均交互的奇异控制平稳平均场博弈，证明了均衡的存在唯一性，并通过阿贝尔极限关联两类博弈，数值示例展示了参数依赖。
We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and ergodic performance criteria. This class of games finds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove the existence and uniqueness of the mean field equilibria, which are completely characterized through nonlinear equations. Furthermore, we relate the mean field equilibria for the discounted and ergodic games by showing the validity of an Abelian limit. The latter also allows us to approximate Nash equilibria of—so far unexplored—symmetric N-player ergodic singular control games through the mean field equilibrium of the discounted game. Numerical examples finally illustrate in a case study the dependency of the mean field equilibria with respect to the parameters of the games. Funding: The authors acknowledge financial support from the Alan Turing Institute and CMAP, École Polytechnique during this project. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 317210226 – SFB 1283.