Minimax Theory and its Applications 08 (2023), No. 1, 001--036
Copyright Heldermann Verlag 2023
A Duality Approach to a Price Formation MFG Model
Yuri Ashrafyan
King Abdullah University of Science and Technology, CEMSE Division, Thuwal, Saudi Arabia
Tigran Bakaryan
King Abdullah University of Science and Technology, CEMSE Division, Thuwal, Saudi Arabia
Diogo Gomes
King Abdullah University of Science and Technology, CEMSE Division, Thuwal, Saudi Arabia
Julian Gutierrez
King Abdullah University of Science and Technology, CEMSE Division, Thuwal, Saudi Arabia
julian.gutierrezpineda@kaust.edu.sa
We study the connection between the Aubry-Mather theory and a mean-field game (MFG) price-formation model. We introduce a framework for Mather measures that is suited for constrained time-dependent problems in R. Then, we propose a variational problem on a space of measures, from which we obtain a duality relation involving the MFG problem examined by D. Gomes and J. Saude [A mean-field game approach to price formation, Dyn. Games Appl. 11/1 (2021) 29--53].
Keywords: Mean field games, price formation, duality, optimal transport.
MSC: 49N90, 91A13, 35F21, 37J50.
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