Under a local second-order strict positivity condition on stationary equilibria, mean field game systems with quadratic Hamiltonians exhibit an exponential turnpike property near those equilibria on tori and Euclidean space, with existence of stable solutions established via fixed-point methods.
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The local Turnpike Property in Mean Field Control and Games with quadratic Hamiltonian
Under a local second-order strict positivity condition on stationary equilibria, mean field game systems with quadratic Hamiltonians exhibit an exponential turnpike property near those equilibria on tori and Euclidean space, with existence of stable solutions established via fixed-point methods.