We study stationary mean eld games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games nds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove existence and uniqueness of the mean eld equilibria, which are completely characterized through nonlinear equations. Furthermore, we relate the mean eld 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
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