Optimal control and potential games in the mean field

Felix Höfer and H. Mete Soner

Stochastic Processes and their Applications, 2026, vol. 199, issue C

Abstract: We study a mean-field optimal control problem with general non-Markovian dynamics that allow both common noise and jumps. We show that its minimizers are Nash equilibria of an associated mean field game of controls. These types of games are potential, and the resulting Nash equilibria are closely linked to McKean-Vlasov equations of Langevin type. Furthermore, as a byproduct of our main result, we obtain the existence of strong common noise equilibria for potential games. To illustrate the general theory, we present several examples, including a mean field game of controls with interactions through a price variable, as well as mean-field Cucker-Smale Flocking and Kuramoto models. We also establish the invariance property of the value function, which is a key ingredient used in our proofs.

Keywords: Mean field control; Mean field games; Potential games (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414926001031
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:199:y:2026:i:c:s0304414926001031

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2026.104971

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().