Say that one information structure is eventually Blackwell sufficient for another if, for every large enough n, an n‐sample from the first is Blackwell sufficient (Blackwell (1951, 1954)) for an n‐sample from the second. This note shows that eventual Blackwell sufficiency lies strictly between (one‐shot) Blackwell sufficiency and the ordering of information structures formulated by Moscarini and Smith (2002), and thus offers a new criterion for comparing experiments. A characterization of eventual Blackwell sufficiency in terms of the one‐shot experiments remains an open question.

Experimental economists currently lack a convention for how to pay subjects in experiments with multiple tasks. We provide a theoretical framework for analyzing this question. Assuming statewise monotonicity and nothing else, we prove that paying for one randomly chosen problem—the random problem selection mechanism—is essentially the only incentive compatible mechanism. Paying for every period is similarly justified when we assume only a “no complementarities at the top” condition. To help experimenters decide which is appropriate for their particular experiment, we discuss empirical tests of these two assumptions.