Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/238128
Year of Publication: 
2021
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 650
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
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 ergodic 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, which are completely characterized through nonlinear equations. Furthermore, we relate 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.
Subjects: 
stationary mean field games
singular control
discounted and ergodic criterion
onedimensional Ito-diffusion
Abelian limit
optimal productivity expansion
Ɛ-Nash equilibrium
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Working Paper

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