Existence and a vanishing-discount selection criterion are proved for quasi-stationary first-order contact mean-field games, with the selected limit given by Peierls barriers.
Cardaliaguet, Long time average of first order mean field games and weak KAM theory, Dyn
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Existence of Solutions and Selection Problem for Quasi-stationary Contact Mean Field Games
Existence and a vanishing-discount selection criterion are proved for quasi-stationary first-order contact mean-field games, with the selected limit given by Peierls barriers.