Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/278277
Authors: 
Year of Publication: 
2023
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 674
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some structural conditions which are related to the submodularity of the underlying mean field game and are a sort of opposite version of the well known Lasry-Lions monotonicity. By reformulating the representative player minimization problem via the stochastic maximum principle, the submodularity conditions allow to prove comparison principles for the forward-backward system, which correspond to the monotonicity of the best reply map. Building on this property, existence of strong solutions is shown via Tarski's fixed point theorem, both for the mean field game and for the related McKean-Vlasov forward-backward system. In both cases, the set of solutions enjoys a lattice structure, with minimal and maximal solutions which can be constructed by iterating the best reply map or via the fictitious play algorithm.
Subjects: 
Mean field games with common noise
FBSDE
Mean field with conditional law
stochastic maximum principle
submodular cost function
Tarski's fixed point theorem
fictitious play
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Working Paper

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