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 [GK14]. 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. [GK14] 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. [GK14] also design a mechanism with PoRM of $O(\ln^2(k))$ for CAII. In this paper, we seek to overcome the impossibility result of [GK14] 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

Learning Prices for Repeated Auctions with Strategic Buyers

Inspired by real-time ad exchanges for online display advertising, we consider the problem of inferring a buyer's value distribution for a good when the buyer is repeatedly interacting with a seller through a posted-price mechanism. We model the buyer as a strategic agent, whose goal is to maximize her long-term surplus, and we are interested in mechanisms that maximize the seller's long-term revenue. We define the natural notion of strategic regret --- the lost revenue as measured against a truthful (non-strategic) buyer. We present seller algorithms that are no-(strategic)-regret when the buyer discounts her future surplus --- i.e. the buyer prefers showing advertisements to users sooner rather than later. We also give a lower bound on strategic regret that increases as the buyer's discounting weakens and shows, in particular, that any seller algorithm will suffer linear strategic regret if there is no discounting.Comment: Neural Information Processing Systems (NIPS 2013

Characterizing Optimal Adword Auctions

We present a number of models for the adword auctions used for pricing advertising slots on search engines such as Google, Yahoo! etc. We begin with a general problem formulation which allows the privately known valuation per click to be a function of both the identity of the advertiser and the slot. We present a compact characterization of the set of all deterministic incentive compatible direct mechanisms for this model. This new characterization allows us to conclude that there are incentive compatible mechanisms for this auction with a multi-dimensional type-space that are {\em not} affine maximizers. Next, we discuss two interesting special cases: slot independent valuation and slot independent valuation up to a privately known slot and zero thereafter. For both of these special cases, we characterize revenue maximizing and efficiency maximizing mechanisms and show that these mechanisms can be computed with a worst case computational complexity $O(n^2m^2)$ and $O(n^2m^3)$ respectively, where $n$ is number of bidders and $m$ is number of slots. Next, we characterize optimal rank based allocation rules and propose a new mechanism that we call the customized rank based allocation. We report the results of a numerical study that compare the revenue and efficiency of the proposed mechanisms. The numerical results suggest that customized rank-based allocation rule is significantly superior to the rank-based allocation rules.Comment: 29 pages, work was presented at a) Second Workshop on Sponsored Search Auctions, Ann Arbor, MI b) INFORMS Annual Meeting, Pittsburgh c) Decision Sciences Seminar, Fuqua School of Business, Duke Universit

Optimising Trade-offs Among Stakeholders in Ad Auctions

We examine trade-offs among stakeholders in ad auctions. Our metrics are the revenue for the utility of the auctioneer, the number of clicks for the utility of the users and the welfare for the utility of the advertisers. We show how to optimize linear combinations of the stakeholder utilities, showing that these can be tackled through a GSP auction with a per-click reserve price. We then examine constrained optimization of stakeholder utilities. We use simulations and analysis of real-world sponsored search auction data to demonstrate the feasible trade-offs, examining the effect of changing the allowed number of ads on the utilities of the stakeholders. We investigate both short term effects, when the players do not have the time to modify their behavior, and long term equilibrium conditions. Finally, we examine a combinatorially richer constrained optimization problem, where there are several possible allowed configurations (templates) of ad formats. This model captures richer ad formats, which allow using the available screen real estate in various ways. We show that two natural generalizations of the GSP auction rules to this domain are poorly behaved, resulting in not having a symmetric Nash equilibrium or having one with poor welfare. We also provide positive results for restricted cases.Comment: 18 pages, 10 figures, ACM Conference on Economics and Computation 201