Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/201646
Authors: 
Dianetti, Jodi
Ferrari, Giorgio
Fischer, Markus
Nendel, Max
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers 621
Abstract: 
We study mean field games with scalar It-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.
Subjects: 
Mean field games
submodular cost function
complete lattice
first order stochastic dominance
Tarski's fixed point theorem
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.