Best response dynamics for continuous zero--sum games
Josef Hofbauer - Department of Mathematics, University College London, London WC1E 6BT, United Kingdom (email)
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.
Keywords: Best response dynamics, fictitious play, minmax theorem, discretization, global attractor.
Received: August 2005; Revised: October 2005; Published: October 2005.
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