We study revenue optimization learning algorithms for repeated posted-price auctions where a seller interacts with a single strategic buyer that holds a fixed private valuation for a good and seeks to maximize his cumulative discounted surplus. For this setting, first, we propose a novel algorithm that never decreases offered prices and has a tight strategic regret bound in @math under some mild assumptions on the buyer surplus discounting. This result closes the open research question on the existence of a no-regret horizon-independent weakly consistent pricing. The proposed algorithm is inspired by our observation that a double decrease of offered prices in a weakly consistent algorithm is enough to cause a linear regret. This motivates us to construct a novel transformation that maps a right-consistent algorithm to a weakly consistent one that never decreases offered prices. Second, we outperform the previously known strategic regret upper bound of the algorithm PRRFES, where the improvement is achieved by means of a finer constant factor @math of the principal term @math in this upper bound. Finally, we generalize results on strategic regret previously known for geometric discounting of the buyer's surplus to discounting of other types, namely: the optimality of the pricing PRRFES to the case of geometrically concave decreasing discounting; and linear lower bound on the strategic regret of a wide range of horizon-independent weakly consistent algorithms to the case of arbitrary discounts.
We describe two auction forms for search engine advertising and present two simple theoretical results concerning i) the estimation of click-through rates and ii) how to adjust the auctions for broad match search. We also describe some of the practical issues involved in implementing a VCG auction.  We present the results of a large field experiment on setting reserve prices in auctions for online advertisements, guided by the theory of optimal auction design suitably adapted to the sponsored search setting. Consistent with the theory, following the introduction of new reserve prices revenues in these auctions have increased substantially.  We performed controlled experiments of human participants in a continuous sequence of ad auctions, similar to those used by Internet companies. The goal of the research was to understand users' strategies in making bids. We studied the behavior under two auction types: (1) the Generalized Second-Price (GSP) auction and (2) the Vickrey--Clarke--Groves (VCG) payment rule, and manipulated also the participants' knowledge conditions: (1) explicitly given valuations and (2) payoff information from which valuations could be deduced. We found several interesting behaviors, among them are: No convergence to equilibrium was detected; moreover the frequency with which participants modified their bids increased with time. We can detect explicit "better-response" behavior rather than just mixed bidding. While bidders in GSP auctions do strategically shade their bids, they tend to bid higher than theoretically predicted by the standard VCG-like equilibrium of GSP. Bidders who are not explicitly given their valuations but can only deduce them from their gains behave a little less "precisely" than those with such explicit knowledge, but mostly during an initial learning phase. VCG and GSP yield approximately the same (high) social welfare, but GSP tends to give higher revenue. We present a two-stage model of competing ad auctions. Search engines attract users via Cournot-style competition. Meanwhile, each advertiser must pay a participation cost to use each ad platform, and advertiser entry strategies are derived using symmetric Bayes-Nash equilibrium that lead to the VCG outcome of the ad auctions. Consistent with our model of participation costs, we find empirical evidence that multi-homing advertisers are larger than single-homing advertisers. We then link our model to search engine market conditions: We derive comparative statics on consumer choice parameters, presenting relationships between market share, quality, and user welfare. We also analyze the prospect of joining auctions to mitigate participation costs, and we characterize when such joins do and do not increase welfare. In sponsored search, a number of advertising slots is available on a search results page, and have to be allocated among a set of advertisers competing to display an ad on the page. This gives rise to a bipartite matching market that is typically cleared by the way of an automated auction. Several auction mechanisms have been proposed, with variants of the Generalized Second Price (GSP) being widely used in practice. There is a rich body of work on bipartite matching markets that builds upon the stable marriage model of Gale and Shapley and the assignment model of Shapley and Shubik. This line of research offers deep insights into the structure of stable outcomes in such markets and their incentive properties. In this paper, we model advertising auctions in terms of an assignment model with linear utilities, extended with bidder and item specific maximum and minimum prices. Auction mechanisms like the commonly used GSP or the well-known Vickrey-Clarke-Groves (VCG) can be interpreted as simply computing a bidder-optimal stable matching in this model, for a suitably defined set of bidder preferences, but our model includes much richer bidders and preferences. We prove that in our model the existence of a stable matching is guaranteed, and under a non-degeneracy assumption a bidder-optimal stable matching exists as well. We give an algorithm to find such matching in polynomial time, and use it to design truthful mechanism that generalizes GSP, is truthful for profit-maximizing bidders, correctly implements features like bidder-specific minimum prices and position-specific bids, and works for rich mixtures of bidders and preferences. Our main technical contributions are the existence of bidder-optimal matchings and strategyproofness of the resulting mechanism, and are proved by induction on the progress of the matching algorithm.  Targeted online advertising is a prime source of revenue for many Internet companies. It is a common industry practice to use a generalized second price auction mechanism to rank advertisements at every opportunity of an impression. This greedy algorithm is suboptimal for both advertisers and publishers when advertisers have a finite budget. In a greedy mechanism high performing advertisers tend to drop out of the auction marketplace fast and that adversely affects both the advertiser experience and the publisher revenue. We describe a method for improving such ad serving systems by including a budget pacing component that serves ads by being aware of global supply patterns. Such a system is beneficial for both advertisers and publishers. We demonstrate the benefits of this component using experiments we conducted on advertising at LinkedIn. We consider the optimization of revenue in advertising auctions based on the generalized second-price (GSP) paradigm, which has become a de facto standard. We examine several different GSP variants (including squashing and different types of reserve prices), and consider how to set their parameters optimally. One intriguing finding is that charging each advertiser the same per-click reserve price ("unweighted reserve prices") yields dramatically more revenue than the quality-weighted reserve prices that have become common practice. This result is robust, arising both from theoretical analysis and from two different kinds of computational experiments. We also identify a new GSP variant that is revenue optimal in restricted settings. Finally, we study how squashing and reserve prices interact, and how equilibrium selection affects the revenue of GSP when features such as reserves or squashing are applied. Auctions are widely used on the Web. Applications range from internet advertising to platforms such as eBay. In most of these applications the auctions in use are single multi-item auctions with unit demand. The main drawback of standard mechanisms for this type of auctions, such as VCG and GSP, is the limited expressiveness that they offer to the bidders. The General Auction Mechanism (GAM) of [1] is taking a first step towards addressing the problem of limited expressiveness by computing a bidder optimal, envy free outcome for linear utility functions with identical slopes and a single discontinuity per bidder-item pair. We show that in many practical situations this does not suffice to adequately model the preferences of the bidders, and we overcome this problem by presenting the first mechanism for piece-wise linear utility functions with non-identical slopes and multiple discontinuities. Our mechanism runs in polynomial time. Like GAM it is incentive compatible for inputs that fulfill a certain non-degeneracy requirement, but our requirement is more general than the requirement of GAM. For discontinuous utility functions that are non-degenerate as well as for continuous utility functions the outcome of our mechanism is a competitive equilibrium. We also show how our mechanism can be used to compute approximately bidder optimal, envy free outcomes for a general class of continuous utility functions via piece-wise linear approximation. Finally, we prove hardness results for even more expressive settings.  We present a simple auction mechanism which extends the second-price auction with reserve and is truthful in expectation. This mechanism is particularly effective in private value environments where the distribution of valuations are irregular. Bidders can "buy-it-now", or alternatively "take-a-chance" where the top d bidders are equally likely to win. The randomized take-a-chance allocation incentivizes high valuation bidders to buy-it-now. We show that for a large class of valuations, this mechanism achieves similar allocations and revenues as Myerson's optimal mechanism, and outperforms the second-price auction with reserve. In addition, we present an evaluation of bid data from Microsoft's AdECN platform. We find the valuations are irregular, and counterfactual experiments suggest our BIN-TAC mechanism would improve revenue by 11 relative to an optimal second-price mechanism with reserve. I describe how search engines sell ad space using an auction. I analyze advertiser behavior in this context using elementary price theory and derive a simple way to estimate the producer surplus generated by online search advertising. It appears that the estimated value of online advertising tends to be between 2 and 2.3 times advertising expenditures. JEL: D44 (Auctions), D21 (Firm Behavior) 