Sequential Peer Prediction: Learning to Elicit Effort using Posted   Prices
  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. 
Yang Liu and Yiling Chen
cs.GT