Stationary Discounted and Ergodic Mean Field Games of Singular Control

Cao H, Dianetti J, Ferrari G (2021) Center for Mathematical Economics Working Papers; 650.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
stationary mean field games; singular control; discounted and ergodic criterion; one-dimensional Itô-diffusion; Abelian limit; optimal productivity expansion; ε-Nash equilibrium
Erscheinungsjahr
2021
Band
650
Seite(n)
29
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2955165

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Cao H, Dianetti J, Ferrari G. Stationary Discounted and Ergodic Mean Field Games of Singular Control. Center for Mathematical Economics Working Papers. Vol 650. Bielefeld: Center for Mathematical Economics; 2021.
Cao, H., Dianetti, J., & Ferrari, G. (2021). Stationary Discounted and Ergodic Mean Field Games of Singular Control (Center for Mathematical Economics Working Papers, 650). Bielefeld: Center for Mathematical Economics.
Cao, H., Dianetti, J., and Ferrari, G. (2021). Stationary Discounted and Ergodic Mean Field Games of Singular Control. Center for Mathematical Economics Working Papers, 650, Bielefeld: Center for Mathematical Economics.
Cao, H., Dianetti, J., & Ferrari, G., 2021. Stationary Discounted and Ergodic Mean Field Games of Singular Control, Center for Mathematical Economics Working Papers, no.650, Bielefeld: Center for Mathematical Economics.
H. Cao, J. Dianetti, and G. Ferrari, Stationary Discounted and Ergodic Mean Field Games of Singular Control, Center for Mathematical Economics Working Papers, vol. 650, Bielefeld: Center for Mathematical Economics, 2021.
Cao, H., Dianetti, J., Ferrari, G.: Stationary Discounted and Ergodic Mean Field Games of Singular Control. Center for Mathematical Economics Working Papers, 650. Center for Mathematical Economics, Bielefeld (2021).
Cao, Haoyang, Dianetti, Jodi, and Ferrari, Giorgio. Stationary Discounted and Ergodic Mean Field Games of Singular Control. Bielefeld: Center for Mathematical Economics, 2021. Center for Mathematical Economics Working Papers. 650.
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2021-05-26T07:53:37Z
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