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arXiv · 2004.06505

Weak KAM approach to first-order Mean Field Games with state constraints

Piermarco Cannarsa·Wei Cheng·Cristian Mendico·Kaizhi Wang
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Abstract

We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon $T$ goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on $[0,T]$ converges to the solution of the ergodic system as $T \to +\infty$.

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Piermarco Cannarsa, Wei Cheng, Cristian Mendico, Kaizhi Wang. 2020-04-14. Weak KAM approach to first-order Mean Field Games with state constraints. https://doi.org/10.1007/s10884-021-10071-9

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