Constrained Mean Field Games Equilibria as Fixed Point of Random Lifting of Set-Valued Maps

Capuani, Rossana; Marigonda, Antonio

doi:10.1016/j.ifacol.2022.11.049

Constrained Mean Field Games Equilibria as Fixed Point of Random Lifting of Set-Valued Maps

Author(s)

Capuani, Rossana

Marigonda, Antonio

Date Issued

2022

Type

conferenceObject

Volume

55

Start Page

180

End Page

185

DOI

10.1016/j.ifacol.2022.11.049

Journal

IFAC-PAPERSONLINE

Abstract

We introduce an abstract framework for the study of general mean field game and mean field control problems. Given a multiagent system, its macroscopic description is provided by a time-depending probability measure, where at every instant of time the measure of a set represents the fraction of (microscopic) agents contained in it. The trajectories available to each of the microscopic agents are affected also by the overall state of the system. By using a suitable concept of random lift of set-valued maps, together with fixed point arguments, we are able to derive properties of the macroscopic description of the system from properties of the set-valued map expressing the admissible trajectories for the microscopical agents. We apply the results in the case in which the admissible trajectories of the agents are the minimizers of a suitable integral functional depending also from the macroscopic evolution of the system

Handle

http://hdl.handle.net/2067/53827

Conference(s)

25th IFAC Symposium on Mathematical Theory of Networks and Systems, MTNS 2022