Submodular Mean Field Games. Existence and Approximation of Solutions

Dianetti J, Ferrari G, Fischer M, Nendel M (2019) Center for Mathematical Economics Working Papers; 621.
Bielefeld: Center for Mathematical Economics.

Download
OA 465.58 KB
Diskussionspapier | Veröffentlicht | Englisch
Volltext vorhanden für diesen Nachweis
Abstract / Bemerkung
We study mean field games with scalar Itô-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences. Firstly, it allows us to prove existence of solutions via an application of Tarski's fixed point theorem, covering cases with discontinuous dependence on the measure variable. Secondly, it ensures that the set of solutions enjoys a lattice structure: in particular, there exist a minimal and a maximal solution. Thirdly, it guarantees that those two solutions can be obtained through a simple learning procedure based on the iterations of the best-response-map. The mean field game is first defined over ordinary stochastic controls, then extended to relaxed controls. Our approach allows also to treat a class of submodular mean field games with common noise in which the representative player at equilibrium interacts with the (conditional) mean of its state's distribution.
Erscheinungsjahr
Band
621
ISSN
PUB-ID

Zitieren

Dianetti J, Ferrari G, Fischer M, Nendel M. Submodular Mean Field Games. Existence and Approximation of Solutions. Center for Mathematical Economics Working Papers. Vol 621. Bielefeld: Center for Mathematical Economics; 2019.
Dianetti, J., Ferrari, G., Fischer, M., & Nendel, M. (2019). Submodular Mean Field Games. Existence and Approximation of Solutions (Center for Mathematical Economics Working Papers, 621). Bielefeld: Center for Mathematical Economics.
Dianetti, J., Ferrari, G., Fischer, M., and Nendel, M. (2019). Submodular Mean Field Games. Existence and Approximation of Solutions. Center for Mathematical Economics Working Papers, 621, Bielefeld: Center for Mathematical Economics.
Dianetti, J., et al., 2019. Submodular Mean Field Games. Existence and Approximation of Solutions, Center for Mathematical Economics Working Papers, no.621, Bielefeld: Center for Mathematical Economics.
J. Dianetti, et al., Submodular Mean Field Games. Existence and Approximation of Solutions, Center for Mathematical Economics Working Papers, vol. 621, Bielefeld: Center for Mathematical Economics, 2019.
Dianetti, J., Ferrari, G., Fischer, M., Nendel, M.: Submodular Mean Field Games. Existence and Approximation of Solutions. Center for Mathematical Economics Working Papers, 621. Center for Mathematical Economics, Bielefeld (2019).
Dianetti, Jodi, Ferrari, Giorgio, Fischer, Markus, and Nendel, Max. Submodular Mean Field Games. Existence and Approximation of Solutions. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 621.
Alle Dateien verfügbar unter der/den folgenden Lizenz(en):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Volltext(e)
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-07-26T08:50:03Z
MD5 Prüfsumme
28b0229ee3101ca1992a5d7e44d26266

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Suchen in

Google Scholar