@booklet {sergiuhart-armwmi2012,
	title = {Approximate Revenue Maximization with Multiple Items},
	howpublished = {Discussion Papers},
	year = {2012},
	month = {4},
	abstract = {Myerson{\textquoteright}s classic result provides a full description of how a seller can maximize revenue when~selling a single item. We address the question of revenue maximization in the simplest possible~multi-item setting: two items and a single buyer who has independently distributed values for theitems, and an additive valuation. In general, the revenue achievable from selling two independent~items may be strictly higher than the sum of the revenues obtainable by selling each of themseparately. In fact, the structure of optimal (i.e., revenue-maximizing) mechanisms for two itemseven in this simple setting is not understood.In this paper we obtain approximate revenue optimization results using two simple auctions: that~of selling the items separately, and that of selling them as a single bundle. Our main results~(which are of a "direct sum" variety, and apply to any distributions) are as follows. Selling theitems separately guarantees at least half the revenue of the optimal auction; for identicallydistributed items, this becomes at least 73\% of the optimal revenue.~For the case of k > 2 items, we show that selling separately guarantees at least a c/log^2 k~fraction of the optimal revenue; for identically distributed items, the bundling auction yields at~least a c/log k fraction of the optimal revenue.},
	url = {http://www.ma.huji.ac.il/hart/abs/m-approx.html},
	author = {Sergiu Hart, Noam Nisan}
}
