The ergodic Mean Field Game system for a type of state constraint condition

Mariya Sardarli

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arXiv · 2101.10564

The ergodic Mean Field Game system for a type of state constraint condition

Mariya Sardarli

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Abstract

This paper investigates the well-posedness of a type of state constraint ergodic Mean Field Game system in a bounded domain in which the Hamilton-Jacobi-Bellman equation is paired with an infinite Dirichlet boundary condition. In this setting, the infinite boundary condition prevents the underlying stochastic trajectories from reaching the boundary, resulting in a state constraint solution. We consider a class of superlinear power-like Hamiltonians and establish existence and uniqueness results under appropriate assumptions on the coupling. We treat both non-local and local couplings, and establish the uniqueness of the system by exploiting the decay of the density near the boundary.

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Mariya Sardarli. 2021-01-26. The ergodic Mean Field Game system for a type of state constraint condition. https://arxiv.org/abs/2101.10564

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