  We study online learning settings in which experts act strategically to
maximize their influence on the learning algorithm's predictions by potentially
misreporting their beliefs about a sequence of binary events. Our goal is
twofold. First, we want the learning algorithm to be no-regret with respect to
the best fixed expert in hindsight. Second, we want incentive compatibility, a
guarantee that each expert's best strategy is to report his true beliefs about
the realization of each event. To achieve this goal, we build on the literature
on wagering mechanisms, a type of multi-agent scoring rule. We provide
algorithms that achieve no regret and incentive compatibility for myopic
experts for both the full and partial information settings. In experiments on
datasets from FiveThirtyEight, our algorithms have regret comparable to classic
no-regret algorithms, which are not incentive-compatible. Finally, we identify
an incentive-compatible algorithm for forward-looking strategic agents that
exhibits diminishing regret in practice.
