Mertens's asymptotic value conjecture for zero-sum repeated games

Let a finite two-person zero-sum repeated game have values $v_n$ for its $n$-stage games and $v_{\lambda}$ for its $\lambda$-discounted games, where $n\in\mathbb{N}^*$ and $\lambda\in(0,1]$. Mertens's asymptotic value conjecture. In a zero-sum repeated game, the asymptotic value exists:

$$\lim_{n\rightarrow +\infty}v_n\quad\text{and}\quad\lim_{\lambda\rightarrow 0}v_{\lambda}$$

exist and are equal. This conjecture concerns the agreement between long-horizon Cesaro and Abel evaluations; the source does not provide evidence resolving it.