I have read several experimental papers which ask people to make decisions which only matter with a certain probability. For example, individuals might be asked to submit bids in an auction, but told that their bids only 'count' with a certain probability $p$ (with probability $1 - p$, their payoff is 0 regardless of what they do). Alternatively, if we wanted to learn whether an individual's valuation for a good exceeds £10, we could offer to sell her that good for £10; but tell her that the good will be sold to her (and the payment taken) only with a certain probability. In both cases, the idea is that individuals should act as they would if $p = 1$ (i.e. the mechanism is 'incentive compatible') which then allows researchers to run these experiments more cheaply than they would be able to otherwise.
Is there any evidence about the general validity of this approach? More concretely, is there evidence as to whether the outputs of such experiments vary with $p$? Intuitively, I would have expected that subjects become inattentive if $p$ is very low (since in absolute terms, it doesn't matter much what they do), which could then add noise to the elicited estimates.