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Generic Uniqueness of the Bias Vector of Mean-Payoff Zero-Sum Games

Antoine Hochart 1, 2 Marianne Akian 2, 1 Stéphane Gaubert 2, 1 
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : Under some ergodicity conditions, finite state space mean payoff zero-sum games can be solved using a nonlinear fixed point problem, involving a vector (bias or potential), which determines the optimal strategies. A basic issue is to check when the bias is unique. We show that this is always the case for generic values of the payments of the game. We also discuss the application of this result to the perturbation analysis of policy iteration.
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Submitted on : Wednesday, January 27, 2016 - 4:42:31 PM
Last modification on : Thursday, January 20, 2022 - 5:27:41 PM


  • HAL Id : hal-01263363, version 1


Antoine Hochart, Marianne Akian, Stéphane Gaubert. Generic Uniqueness of the Bias Vector of Mean-Payoff Zero-Sum Games. SIAM Conference on Control and its Applications (SIAM CT’15), Jul 2015, Paris, France. ⟨hal-01263363⟩



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