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We study two-player zero-sum recursive games with a countable state space andfinite action spaces at each state. When the family of $n$-stage values$\{v_n,n\geq 1\}$ is totally bounded for the uniform norm, we prove theexistence of the uniform value. Together with a result in Rosenberg and Vieille(2000), we obtain a uniform Tauberian theorem for recursive games: $(v_n)$converges uniformly if and only if $(v_\lambda)$ converges uniformly.  We apply our main result to finite recursive games with signals (whereplayers observe only signals on the state and on past actions). When themaximizer is more informed than the minimizer, we prove the Mertens conjecture$Maxmin=\lim_{n\to\infty} v_n=\lim_{\lambda\to 0}v_\lambda$. Finally, we deducethe existence of the uniform value in finite recursive game with symmetricinformation.

Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture "$Maxmin=\lim v_n=\lim v_\lambda$"