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arXiv · 1904.13287

Weak KAM theory for potential MFG

Pierre Cardaliaguet·Marco Masoero
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Abstract

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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Pierre Cardaliaguet, Marco Masoero. 2019-04-30. Weak KAM theory for potential MFG. https://arxiv.org/abs/1904.13287

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