Procurement without Priors: A Simple Mechanism and its Notable Performance

How should a buyer design procurement mechanisms when suppliers' costs are unknown, and the buyer does not have a prior belief? We demonstrate that simple mechanisms - that share a constant fraction of the buyer utility with the seller - allow the buyer to realize a guaranteed positive fraction of the efficient social surplus across all possible costs. Moreover, a judicious choice of the share based on the known demand maximizes the surplus ratio guarantee that can be attained across all possible (arbitrarily complex and nonlinear) mechanisms and cost functions. Similar results hold in related nonlinear pricing and optimal regulation problems.