Best response dynamics for continuous zero--sum games
sylvain sorin2005, Discrete and Continuous Dynamical Systems-series B
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Abstract
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.
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