Limited Supply Online Auctions for Revenue Maximization

Abstract

We consider the design of competitive truthful auctions for prior-free revenue maximization, to sell copies of a single good in limited supply to unit-demand bidders that arrive online. The online model, first studied in [Hajiaghayi, Kleinberg, Parkes, ACM EC 2004] and recently revisited in [Koutsoupias and Pierrakos, WINE 2010], is reminiscent of the secretary problem, in that the order of the bidders’ arrival is chosen uniformly at random. The benchmark against which the generated revenue is compared is the one introduced by Goldberg et al. [Games and Economic Behavior 55(2):242–269, 2006]. We consider two variants of limited supply; a hard constraint of k available copies and convex production cost curve for each copy. For each case we present an algorithmic reduction of the problem to the problem of unlimited supply studied by Koutsoupias and Pierrakos. Our reduction for the case of k available copies yields a 26e-competitive auction thus improving significantly upon the best known ratio of 6338, from [Hajiaghayi, Kleinberg, Parkes, ACM EC 2004].

Work partially supported by EPSRC grants EP/F069502/1 and EP/G069239/1 and by GSRT, Greece, within the action ”Supporting Postdoctoral Researchers” (PE6-213 ”DDCOD”), co-financed by the ESF and the Greek State.