Monotone solutions for mean field games master equations: continuous state space and common noise

We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 48; no. 10-12; pp. 1245 - 1285
Main Author Bertucci, Charles
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.12.2023
Taylor & Francis Ltd
Subjects
Analysis of PDEs
Games
Master equation
Mathematical analysis
Mathematics
Mean Field Games
Weak solutions
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ISSN0360-5302
1532-4133
DOI10.1080/03605302.2023.2276564

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Summary:We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the measure argument, in the case of first order master equations. We study several structures of common noises, in particular ones in which common jumps (or aggregate shocks) can happen randomly, and ones in which the correlation of randomness is carried by an additional parameter.
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ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2023.2276564