Nonexistence of constant globally optimal adversary strategies for at least six experts

Let $n$ be the number of experts, and let $\mathbb{S}_n$ denote the sector under consideration. A strategy is constant on the sector if the adversary uses the same strategy throughout $\mathbb{S}_n$.

Constant-strategy nonexistence conjecture. For $n\geq 6$ experts, there is no globally asymptotically optimal adversary strategy that is constant on $\mathbb{S}_n$. The paper reports strong numerical evidence for this phenomenon for $6\leq n\leq 10$, but the general assertion remains open.