A central result in the rational learning literature is that if the true measure is absolutely continuous with respect to the beliefs then, given enough data, the updated beliefs merge with the true distribution. In this paper, we show that, under absolute continuity, weak merging occurs fast...

In a repeated two-person zero-sum game with incomplete information on one side, the values vn of the n-stage games converge to the value v\infty of the infinite game with worst case error \sim(ln n/n)1/3.