Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "

Xiaoxi Li; Xavier Venel

doi:10.1007/s00182-015-0496-4

Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "

Xiaoxi Li ¹ Xavier Venel ^{2, 3}

1 Department of Computer Science - Zhejiang University

2 CES - Centre d'économie de la Sorbonne

3 PSE - Paris School of Economics

Abstract : We study two-player zero-sum recursive games with a countable state space and finite action spaces at each state. When the family of n-stage values {v_n;n >0} is totally bounded for the uniform norm, we prove the existence of the uniform value. Together with a result in Rosenberg and Vieille [12], we obtain a uniform Tauberian theorem for recursive game: (v_n) converges uniformly if and only if (v_λ) converges uniformly. We apply our main result to finite recursive games with signals (where players observe only signals on the state and on past actions). When the maximizer is more informed than the minimizer, we prove the Mertens conjecture Maxmin = lim v_n = lim v_λ. Finally, we deduce the existence of the uniform value in finite recursive games with symmetric information.

Keywords : Tauberian theorem Asymptotic value Uniform value Stochastic games Recursive games

Document type :

Journal articles

Domain :

Mathematics [math] / Optimization and Control [math.OC]

Humanities and Social Sciences / Economies and finances

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Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "

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