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# Best response dynamics for continuous zero--sum games

• We study best response dynamics in continuous time for continuous concave-convex zero-sum games and prove convergence of its trajectories to the set of saddle points, thus providing a dynamical proof of the minmax theorem. Consequences for the corresponding discrete time process with small or diminishing step-sizes are established, including convergence of the fictitious play procedure.
Mathematics Subject Classification: Primary: 34A60, 91A05 ; Secondary: 49J53, 91A22.

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