Bertucci, Charles Monotone solutions for mean field games master equations: finite state space and optimal stopping. (Solutions monotones des équations maîtresses des jeux à champ moyen.) (English. French summary) Zbl 1472.35394 J. Éc. Polytech., Math. 8, 1099-1132 (2021). Summary: We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We first prove results of uniqueness and stability for such solutions. It turns out that this notion is helpful to characterize the value function of mean field games of optimal stopping or impulse control and this is the topic of the second half of this paper. The notion of solution we introduce is only useful in the monotone case. In this article we focus on the finite state space case. Cited in 1 ReviewCited in 17 Documents MSC: 35Q89 PDEs in connection with mean field game theory 35F50 Systems of nonlinear first-order PDEs 91A16 Mean field games (aspects of game theory) Keywords:partial differential equations; mean field games × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Achdou, Yves; Capuzzo-Dolcetta, Italo, Mean field games: numerical methods, SIAM J. Numer. Anal., 48, 3, 1136-1162 (2010) · Zbl 1217.91019 · doi:10.1137/090758477 [2] Achdou, Yves; Laurière, Mathieu, Mean field games and applications: numerical aspects (2020) · Zbl 1457.91057 [3] Briceño-Arias, L.; Kalise, D.; Kobeissi, Z.; Laurière, M.; Mateos González, Á.; Silva, F. 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