Generic Properties of First-Order Mean Field Games

Alberto Bressan () and Khai T. Nguyen ()
Additional contact information
Alberto Bressan: Penn State University
Khai T. Nguyen: North Carolina State University

Dynamic Games and Applications, 2023, vol. 13, issue 3, No 3, 750-782

Abstract: Abstract We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point of view of generic theory. Within a suitable topological space of dynamics and cost functionals, we prove that, for “nearly all” mean field games (in the Baire category sense) the best reply map is single-valued for a.e. player. As a consequence, the mean field game admits a strong (not randomized) solution. Examples are given of open sets of games admitting a single solution, and other open sets admitting multiple solutions. Further examples show the existence of an open set of MFG having a unique solution which is asymptotically stable w.r.t. the best reply map, and another open set of MFG having a unique solution which is unstable. We conclude with an example of a MFG with terminal constraints which does not have any solution, not even in the mild sense with randomized strategies.

Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13235-022-00487-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:dyngam:v:13:y:2023:i:3:d:10.1007_s13235-022-00487-3

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/13235

DOI: 10.1007/s13235-022-00487-3

Access Statistics for this article

Dynamic Games and Applications is currently edited by Georges Zaccour

More articles in Dynamic Games and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().