Jodi Dianetti will visit the Université de Paris (Paris Diderot - LPSM) from February, 28th to March 4th, 2022. During this stay, he will give a talk at on March 3rd, 2022, entitled "Submodular mean field games: Existence and approximation of solutions".

Abstract:
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. Our approach also allows to treat submodular mean field games with common noise, as well as mean field games with singular controls, optimal stopping and reflecting boundary conditions.
This talks is based on some joint works together with Giorgio Ferrari, Markus Fischer and Max Nendel.