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Pré-Publication, Document De Travail Année : 2019

Weak KAM theory for potential MFG

Résumé

We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to infinity, of the value function of an optimal control problem stated in the space of measures. In addition, we show a mean field limit for the ergodic constant associated with the corresponding Hamilton-Jacobi equation.
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Dates et versions

hal-02116125 , version 1 (30-04-2019)

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  • HAL Id : hal-02116125 , version 1

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Pierre Cardaliaguet, Marco Masoero. Weak KAM theory for potential MFG. 2019. ⟨hal-02116125⟩
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