  Beginning with Witkowski et al. [2022], recent work on forecasting
competitions has addressed incentive problems with the common winner-take-all
mechanism. Frongillo et al. [2021] propose a competition mechanism based on
follow-the-regularized-leader (FTRL), an online learning framework. They show
that their mechanism selects an $\epsilon$-optimal forecaster with high
probability using only $O(\log(n)/\epsilon^2)$ events. These works, together
with all prior work on this problem thus far, assume that events are
independent. We initiate the study of forecasting competitions for correlated
events. To quantify correlation, we introduce a notion of block correlation,
which allows each event to be strongly correlated with up to $b$ others. We
show that under distributions with this correlation, the FTRL mechanism retains
its $\epsilon$-optimal guarantee using $O(b^2 \log(n)/\epsilon^2)$ events. Our
proof involves a novel concentration bound for correlated random variables
which may be of broader interest.
