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An existence result for a class of mean field games of controls is provided.In the considered model, the cost functional to be minimized by each agentinvolves a price depending at a given time on the controls of all agents and acongestion term. The existence of a classical solution is demonstrated with theLeray-Schauder theorem; the proof relies in particular on a priori bounds forthe solution, which are obtained with the help of a potential formulation ofthe problem.

Schauder Estimates for a Class of Potential Mean Field Games of Controls