Fast algorithms for computing interim allocations in single-parameter environments

Abstract

Myerson’s seminal work characterized optimal auctions; applied naively, however, his approach yields exponential-time algorithms. Using Border’s theorem, in contrast, one can solve mechanism design problems in polynomial time. This latter approach relies on linear programming machinery, the mechanics of which are significantly more complicated than Myerson’s. Motivated by the simplicity and transparency of Myerson’s analysis, we present fast algorithms for computing interim allocations in simple auction settings. These methods apply to both surplus and revenue maximization, and yield ex-ante symmetric solutions.