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Stationary Discounted and Ergodic Mean Field Games of Singular Control

Haoyang Cao, Jodi Dianetti and Giorgio Ferrari
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Haoyang Cao: Center for Mathematical Economics, Bielefeld University
Jodi Dianetti: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University

No 650, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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 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.

Keywords: stationary mean field games; singular control; discounted and ergodic criterion; one-dimensional Itô-diffusion; Abelian limit; optimal productivity expansion; ε-Nash equilibrium (search for similar items in EconPapers)
Pages: 29
Date: 2021-05-26
New Economics Papers: this item is included in nep-gth
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https://pub.uni-bielefeld.de/download/2955165/2955166 First Version, 2021 (application/pdf)

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