Weak KAM Approach to First-Order Mean Field Games with State Constraints
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AbstractWe 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 goes to infinity.
2013 ◽
Vol 3
(4)
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pp. 473-488
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2018 ◽
Vol 35
(6)
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pp. 1557-1576
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