  We study a generalization of the online binary prediction with expert advice
framework where at each round, the learner is allowed to pick $m\geq 1$ experts
from a pool of $K$ experts and the overall utility is a modular or submodular
function of the chosen experts. We focus on the setting in which experts act
strategically and aim to maximize their influence on the algorithm's
predictions by potentially misreporting their beliefs about the events. Among
others, this setting finds applications in forecasting competitions where the
learner seeks not only to make predictions by aggregating different forecasters
but also to rank them according to their relative performance. Our goal is to
design algorithms that satisfy the following two requirements: 1)
$\textit{Incentive-compatible}$: Incentivize the experts to report their
beliefs truthfully, and 2) $\textit{No-regret}$: Achieve sublinear regret with
respect to the true beliefs of the best fixed set of $m$ experts in hindsight.
Prior works have studied this framework when $m=1$ and provided
incentive-compatible no-regret algorithms for the problem. We first show that a
simple reduction of our problem to the $m=1$ setting is neither efficient nor
effective. Then, we provide algorithms that utilize the specific structure of
the utility functions to achieve the two desired goals.
