A Note on Approximate Revenue Maximization with Two Items

We consider the problem of maximizing revenue when selling 2 items to a single buyer with known valuation distributions. In [1], Hart and Nisan showed that selling each item separately using the optimal Myerson’s price, gains at least half of the revenue attainable by optimal auction for two items. We show that in case the items have different revenues when sold separately the bound can be tightened.