Maximal Revenue with Multiple Goods: Nonmonotonicity and Other Observations

Consider the problem of maximizing the revenue from selling a number of goods to a single buyer. We show that, unlike the case of one good, when the buyer’s values for the goods increase the seller’s maximal revenue may well decrease. Next, through simple and transparent examples, we clarify the need for and the use of randomization when maximizing revenue in the multiple-good versus the one-good case. Finally, we provide a characterization of revenue-maximizing mechanisms (more generally, of “seller-favorable” mechanisms) that circumvents nondifferentiability issues. Previous versions: June 2011, November 2012 (Center for Rationality DP-630). See http://www.ma.huji.ac.il/hart/abs/2good-p.html for a presentation that includes some of the results of this paper. Research partially supported by the National Science Foundation (SES-0922535, SES-1227506) and the European Research Council (FP7249159). The authors thank Bob Aumann, Elchanan Ben-Porath, Eddie Dekel, Alex Gershkov, Ilan Kremer, Noam Nisan, Motty Perry, Eyal Winter, and Asher Wolinsky for useful discussions and suggestions. Department of Economics, Institute of Mathematics, and Center for the Study of Rationality, The Hebrew University of Jerusalem. E-mail : [email protected] Web site: http://www.ma.huji.ac.il/hart Department of Economics, University of Chicago. E-mail : [email protected] Web site: http://home.uchicago.edu/~preny