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. Copyright (C) 2022 The Authors.

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

Capuani, R;Marigonda, A
2022-01-01

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. Copyright (C) 2022 The Authors.
2022
Multi-agents system
Differential or dynamic games
Set-valued map
Mean Field Games
state constraints
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S2405896322026829-main.pdf

accesso aperto

Descrizione: Full text
Tipologia: Versione dell'editore
Licenza: Creative commons
Dimensione 453.93 kB
Formato Adobe PDF
453.93 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1099686
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact