Existence of a solution to an equation arising from the theory of Mean Field Games

We construct a small time strong solution to a nonlocal Hamilton Jacobi equation (1.1) introduced in [481, the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton Jacobi equations studied in [2,19,20] and solutions to (1. 1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in 148], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2). (C) 2015 Elsevier Inc. All rights reserved.