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.
Origin : Files produced by the author(s)
Loading...