I develop a simplicity criterion for mechanism design, based on belief precision, the number of moments of a type distribution required to compute equilibrium strategies. Focusing on a class of multidimensional procurement auctions called first-score auctions, I show a sharp dichotomy: these mechanisms either have belief precision of two or require full distributional knowledge. This distinction is governed by whether the auction satisfies the fixed-order property, which ensures that the ex post allocation ranking of types is invariant across distributions. I then provide a simple, equilibrium-free test to determine whether a first-score auction has belief precision two. Finally, I microfound the concept by introducing a prior-free game with information acquisition: when agents learn from realistic signal structures about their opponents’ types, first-score auctions with low belief precision are exactly those that admit robust equilibria. The results offer a framework to compare mechanisms along a dimension of strategic simplicity that is closely tied to the informational demands on agents and provides guidance for the design of scoring rules in practice.

(with Ben Brooks and Songzi Du) We consider the design of optimal auctions when buyers may have asymmetric and/or interdependent values. All that is known to the seller is each buyer’s ex ante expected value and an upper bound on the values. We describe a new class of mech anisms which we term compound proportional auctions: Each buyer submits a bid, which is a non-negative real number. The auction then clears in a series of rounds. Within each round, a proportional auction (Brooks and Du, 2021) is run allocate the remaining supply that is left over from previous rounds, among a set of active buyers. At the end of the round, those active buyers with the lowest expected value become inactive. Our main result is that compound proportional auctions maximize the revenue guarantee: minimum expected revenue across all information structures and Bayes Nash equilibria