Mapping an information design game into an all-pay auction

I formally establish the existence of a mapping between a class of information design games with multiple senders and a class of all-pay auctions. I fully characterize this mapping and show how to use it to find equilibria in the information design game. The mapping allows for a straightforward comparative statics analysis of equilibria in the latter class of games. I use it to study the effect of the tie-breaking rule on the distributions of posteriors and the receiver’s payoff.