Mertens's maxmin conjecture for more-informed repeated games

Consider a finite two-person zero-sum repeated game with values $v_n$ for its $n$-stage games and $v_{\lambda}$ for its $\lambda$-discounted games. Player 1 is more informed than Player 2 when Player 1 observes everything that Player 2 observes. Mertens's maxmin conjecture. In a zero-sum repeated game where Player 1 is more informed than Player 2, the sequences $(v_n)$ and $(v_{\lambda})$ converge to the $\operatorname{maxmin}$ of the game, defined as the maximal amount that Player 1 can guarantee for herself in long games. This conjecture predicts that both long-run evaluations equal the informed player's long-run guarantee; the source provides no evidence resolving it.