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