  Peer prediction mechanisms are often adopted to elicit truthful contributions
from crowd workers when no ground-truth verification is available. Recently,
mechanisms of this type have been developed to incentivize effort exertion, in
addition to truthful elicitation. In this paper, we study a sequential peer
prediction problem where a data requester wants to dynamically determine the
reward level to optimize the trade-off between the quality of information
elicited from workers and the total expected payment. In this problem, workers
have homogeneous expertise and heterogeneous cost for exerting effort, both
unknown to the requester. We propose a sequential posted-price mechanism to
dynamically learn the optimal reward level from workers' contributions and to
incentivize effort exertion and truthful reporting. We show that (1) in our
mechanism, workers exerting effort according to a non-degenerate threshold
policy and then reporting truthfully is an equilibrium that returns highest
utility for each worker, and (2) The regret of our learning mechanism w.r.t.
offering the optimal reward (price) is upper bounded by $\tilde{O}(T^{3/4})$
where $T$ is the learning horizon. We further show the power of our learning
approach when the reports of workers do not necessarily follow the
game-theoretic equilibrium.
