Open-loop and closed-loop Nash equilibria of N-player Mean Field Games of Controls converge to the mean field equilibrium at explicit rates under displacement monotonicity, without assuming separable Hamiltonians.
New Uniqueness Results For A Mean Field Game Of Controls
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abstract
We propose a new approach to proving the uniqueness of solutions to a certain class of mean field games of controls. In this class, the equilibrium is determined by an aggregate quantity $Q(t)$, e.g. the market price or production, which then determines optimal trajectories for agents. Our approach consists in analyzing the relationship between $Q(t)$ and corresponding optimal trajectories to find conditions under which there is at most one equilibrium. We show that our conditions do not match those prescribed by the Lasry-Lions monotonicity condition, nor even displacement monotonicity, but they do apply to economic models that have been proposed in the literature.
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Quantitative convergence for displacement monotone Mean Field Games of control
Open-loop and closed-loop Nash equilibria of N-player Mean Field Games of Controls converge to the mean field equilibrium at explicit rates under displacement monotonicity, without assuming separable Hamiltonians.