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The main purpose of this paper is to approximate several non-local evolutionequations by zero-sum repeated games in the spirit of the previous works ofKohn and the second author (2006 and 2009): general fully non-linear parabolicintegro-differential equations on the one hand, and the integral curvature flowof an interface (Imbert, 2008) on the other hand. In order to do so, we startby constructing such a game for eikonal equations whose speed has anon-constant sign. This provides a (discrete) deterministic controlinterpretation of these evolution equations. In all our games, two playerschoose positions successively, and their final payoff is determined by theirpositions and additional parameters of choice. Because of the non-locality ofthe problems approximated, by contrast with local problems, their choices haveto "collect" information far from their current position. For integralcurvature flows, players choose hypersurfaces in the whole space and positionson these hypersurfaces. For parabolic integro-differential equations, playerschoose smooth functions on the whole space.

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations