Randomized Revenue Monotone Mechanisms for Online Advertising

Online advertising is the main source of revenue for many Internet firms. A central component of online advertising is the underlying mechanism that selects and prices the winning ads for a given ad slot. In this paper we study designing a mechanism for the Combinatorial Auction with Identical Items (CAII) in which we are interested in selling k identical items to a group of bidders each demanding a certain number of items between 1 and k. CAII generalizes important online advertising scenarios such as image-text and video-pod auctions [5]. In image-text auction we want to fill an advertising slot on a publisher’s web page with either k text-ads or a single image-ad and in video-pod auction we want to fill an advertising break of k seconds with video-ads of possibly different durations. Our goal is to design truthful mechanisms that satisfy Revenue Monotonicity (RM). RM is a natural constraint which states that the revenue of a mechanism should not decrease if the number of participants increases or if a participant increases her bid. In a recent work Goel and Khani [5], it was argued that RM is a desired property to have for smooth functioning of a firm. Since popular mechanisms like VCG are not revenue-monotone, they introduced the notion of Price of Revenue Monotonicity (PoRM) to capture the loss in social welfare of a revenue-monotone mechanism. Goel and Khani [5] showed that no deterministic RM mechanism can attain PoRM of less than ln(k) for CAII, i.e., no deterministic mechanism can attain more than 1 ln(k) fraction of the maximum social welfare. Goel and Khani [5] also design a mechanism with PoRM of O(ln(k)) for CAII. In this paper, we seek to overcome the impossibility result of Goel and Khani [5] for deterministic mechanisms by using the power of randomization. We show that by using randomization, one can attain a constant PoRM. In particular, we design a randomized RM mechanism with PoRM of 3 for CAII. Finally we study Multi-group Combinatorial Auction with Identical Items (MCAII) which is an important generalization of CAII. In MCAII the bidders are partitioned into multiple groups and the set of winners should be from a single group. The motivation for MCAII is from online advertising scenarios where, for instance, the set of selected ads may be required ? supported in part by NSF CAREER award 1053605, ONR YIP award N000141110662, DARPA/AFRL award FA8650-11-1-7162. ar X iv :1 50 7. 00 13 0v 1 [ cs .G T ] 1 J ul 2 01 5 to have the same format. We give a randomized mechanism which satisfies RM and IC and has PoRM of O(ln k). This is in contrast to log(k) deterministic mechanism that follows from [5].