# American Institute of Mathematical Sciences

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

## Best response dynamics for continuous zero--sum games

 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

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.
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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