Randomized Revenue Monotone Mechanisms for Online Advertising

Abstract

Online advertising is the main source of revenue for many Internet firms; thus designing effective mechanisms for selecting and pricing ads become an important research question. In this paper, we seek to design truthful mechanisms for online advertising that satisfy Revenue Monotonicity (RM) - a natural property which states that the revenue of a mechanism should not decrease if the number of participants increase or if a participant increases her bid. In a recent work [5], it was argued that RM is a desired goal for proper functioning of an online advertising business. 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. [5] then studied the price of revenue-monotonicity of Combinatorial Auction with Identical Items(CAII). In CAII, there are k identical items to be sold to a group of bidders, where bidder i wants either exactly d _i  ∈ {1, …, k} number of items or nothing. CAII generalizes important online advertising scenarios such as image-text and video-pod auctions. In an image-text auction we want to fill an advertising slot with either k text-ads or a single image-ad. In video-pod auction we want to fill a video advertising break of k seconds with video-ads of possibly different durations. [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 $\frac{1}{\ln(k)}$ fraction of the maximum social welfare. [5] also design a mechanism with PoRM of O(ln ²(k)) for CAII.

In this paper, first we overcome the impossibility result of [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. Then, we study a more general Multi-group Combinatorial Auction with Identical Items (MCAII). In MCAII, the bidders are partitioned into multiple groups, and the set of winners are constrainted to be from a single group. The motivation for MCAII is from scenarios where the set of selected ads may be required 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 log²(k) deterministic mechanism that follows from [5].