Dear All,

This Friday, Jodi Dianetti (Center for Mathematical Economics, Bielefeld University) will give a seminar talk on Submodular mean field games, which will be held in person and online via Zoom.

* Place: room 2BC30 at the Department of Mathematics, University of Padova
(Torre Archimede, via Trieste, 63, 35121 Padova)

* Zoom link: please visit the webpage https://www.math.unipd.it/~bianchi/seminari/

* Title: 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.

On behalf of the organizers,

Markus Fischer

Dipartimento di Matematica "Tullio Levi-Civita"