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Their heterogeneous interactions are represented with a graphon, which can be viewed as the limit of a dense random graph. A player\u2019s transition rates between the states depend on their control and the strength of interaction with the other players. We develop a rigorous mathematical framework for the game and analyze Nash equilibria. We provide a sufficient condition for a Nash equilibrium and prove existence of solutions to a continuum of fully coupled forward-backward ordinary differential equations characterizing Nash equilibria. 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