Ridge distributions and information design in simultaneous all-pay auction contests

Two privately informed contestants compete in a contest, and the organizer ex-ante designs a public anonymous disclosure policy to maximize the contestants' total effort. We fully characterize ridge distributions, under which the organizer achieves the first-best outcome in equilibrium: the allocation is efficient, and the entire surplus goes to the organizer. When the prior is a mixture of a ridge distribution and a perfectly correlated distribution, the first-best outcome is achievable by a signal that solely generates ridge distributions as posteriors.