Best response dynamics  for continuous zero--sum games

Josef Hofbauer; Sylvain Sorin

doi:10.3934/dcdsb.2006.6.215

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2006, Volume 6, Issue 1: 215-224. Doi: 10.3934/dcdsb.2006.6.215

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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
2.
Laboratoire d'Econométrie, Ecole Polytechnique, 1 rue Descartes, 75005 Paris

Received: July 31, 2005

Revised: September 30, 2005

Published: December 2005

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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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Mathematics Subject Classification: Primary: 34A60, 91A05 ; Secondary: 49J53, 91A22.

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