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Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "
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.
Cited literature [20 references]
https://hal-paris1.archives-ouvertes.fr/hal-01302553
Contributor : Xavier Venel Connect in order to contact the contributor
Submitted on : Thursday, April 14, 2016 - 3:28:16 PM
Last modification on : Wednesday, November 17, 2021 - 12:33:04 PM
Long-term archiving on: : Friday, July 15, 2016 - 1:10:56 PM
Contributor : Xavier Venel Connect in order to contact the contributor
Submitted on : Thursday, April 14, 2016 - 3:28:16 PM
Last modification on : Wednesday, November 17, 2021 - 12:33:04 PM
Long-term archiving on: : Friday, July 15, 2016 - 1:10:56 PM
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1506.00949v1.pdf
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