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

Abstract We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation (1.1) introduced in [48] , 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  [48] , and make a more rigorous connection between the master equation  (1.1) and the Mean Field Games equations  (1.2) .

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