Best response dynamics for continuous zero--sum games

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January 2006, 6(1): 215-224. doi: 10.3934/dcdsb.2006.6.215

Best response dynamics for continuous zero--sum games

Josef Hofbauer ^1, and Sylvain Sorin ^2,

1.	Department of Mathematics, University College London, London WC1E 6BT, United Kingdom
2.	Laboratoire d'Econométrie, Ecole Polytechnique, 1 rue Descartes, 75005 Paris, France

Received August 2005 Revised October 2005 Published October 2005

Abstract
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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: discretization, global attractor., fictitious play, minmax theorem, Best response dynamics.

Mathematics Subject Classification: Primary: 34A60, 91A05 ; Secondary: 49J53, 91A2.

Citation: Josef Hofbauer, Sylvain Sorin. Best response dynamics for continuous zero--sum games. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 215-224. doi: 10.3934/dcdsb.2006.6.215

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