Optimal approximation constant for simple revenue mechanisms

Determine the optimal universal constant c such that, for a single additive buyer with independently distributed item values, c\,\max(\operatorname{SRev},\operatorname{BRev})\geq\operatorname{OPT}, where \operatorname{SRev} is the optimal revenue from selling items separately, \operatorname{BRev} is the optimal revenue from selling the grand bundle, and \operatorname{OPT} is the revenue of the optimal mechanism.

Background

The paper studies a single additive buyer whose values for multiple items are independently distributed. The two simple mechanisms considered are separate-item pricing and grand-bundle pricing; their revenues are denoted by SRev and BRev, respectively. The optimal mechanism may be randomized and arbitrarily complex, with revenue denoted by OPT.

Prior work improved the upper-bound approximation factor from 6 to 5.2. The paper further improves the upper bound to 3.52, while noting that the best known lower bound on the approximation ratio is 2. The exact optimal constant separating these quantities therefore remains unresolved.