Hypoelliptic Mean Field Games – a Case Study
Keywords:
Mean-Field Games, stationary problems, hypoelliptic operator, eigenvalue problems.Abstract
We study hypoelliptic mean-field games (MFG) that arise in stochastic control problems of degenerate diffusions. Here, we consider MFGs with quadratic Hamiltonians and prove the existence and uniqueness of solutions. Our main tool is the Hopf-Cole transform that converts the MFG into an eigenvalue problem. We prove the existence of a principal eigenvalue and a positive eigenfunction, which are then used to construct the unique solution to the original MFG.
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