Abstract:The paper considers a forward-backward system of parabolic PDEs arising in a Mean Field Game (MFG) model where every agent controls the drift of a trajectory subject to Brownian diffusion, trying to escape a given bounded domain Ω in minimal expected time. The important point is that agents are constrained by a bound on the drift depending on the density of the other agents at their location (the higher the density, the smaller the velocity). Existence for a finite time horizon T is proven via a fixed point ar… Show more
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