TY - GEN AB - 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 an erodic performance criterion. This class of games finds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove existence and uniqueness of the mean field equilibria for the discounted and the ergodic games by showing the validity of an Abelian limit. The latter allows also 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. DA - 2021 KW - stationary mean field games KW - singular control KW - discounted and ergodic criterion KW - one-dimensional Itô-diffusion KW - Abelian limit KW - optimal productivity expansion KW - ε-Nash equilibrium LA - eng PY - 2021 SN - 0931-6558 SP - 29- TI - Stationary Discounted and Ergodic Mean Field Games of Singular Control UR - https://nbn-resolving.org/urn:nbn:de:0070-pub-29551658 Y2 - 2024-11-22T03:00:47 ER -