A Note on the Ratio of Revenues Between Selling in a Bundle and Separately

We consider the problem of maximizing revenue when selling k items to a single buyer with known valuation distributions. Hart and Nisan [2] raised some questions on the approximation of maximizing revenue from selling a set of items by selling each item separately or all in a bundle. In this work we show that for a single, additive buyer whose valuations for for the items are distributed according to i.i.d. distributions which are known to the seller, the ratio of revenue from selling in a bundle to selling separately is at least 55.9% and this gap is attainable.