Submodular mean field games : existence and approximation of solutions / Jodi Dianetti, Giorgio Ferrari, Markus Fischer, and Max Nendel
VerfasserDianetti, Jodi ; Ferrari, Giorgio ; Fischer, Markus ; Nendel, Max
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, July 2019
Elektronische Ressource
Umfang1 Online-Ressource (22 Seiten)
SerieCenter for Mathematical Economics Working papers ; 621
 Das Dokument ist öffentlich im Netz zugänglich.
Submodular mean field games [0.44 mb]

We study mean field games with scalar It^o-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.

 Das Medienwerk ist im Rahmen des deutschen Urheberrechts nutzbar.