A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games

2015/01/26 by Bruno Ziliotto, Ziliotto, Bruno · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Decision-Making and Behavioral Economics #Economic theories and models #Game Theory and Voting Systems #math.OC #msc:47N10 #msc:91A05 #msc:91A15 #msc:91A20 #msc:91A25

paper · pdf · doi:10.48550/arxiv.1501.06525

arxiv created 2015/02/23 · arxiv updated 2015/02/24

Abstract

We prove a Tauberian theorem for nonexpansive operators, and apply it to the model of zero-sum stochastic game. Under mild assumptions, we prove that the value of the lambda-discounted game v_lambda converges uniformly when lambda goes to 0 if and only if the value of the n-stage game v_n converges uniformly when n goes to infinity. This generalizes the Tauberian theorem of Lehrer and Sorin (1992) to the two-player zero-sum case. We also provide the first example of a stochastic game with public signals on the state and perfect observation of actions, with finite state space, signal sets and action sets, in which for some initial state k₁ known by both players, (v_lambda(k₁)) and (v_n(k₁)) converge to distinct limits.

Cited by

• Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture "Maxmin=lim v_n=lim v_λ"

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