How should players bid in keyword auctions such as those used by Google, Yahoo! and MSN? We consider greedy bidding strategies for a repeated auction on a single keyword, where in each round, each player chooses some optimal bid for the next round, assuming that the other players merely repeat their previous bid. We study the revenue, convergence and robustness properties of such strategies. Most interesting among these is a strategy we call the balanced bidding strategy (bb): it is known that bb has a unique fixed point with payments identical to those of the VCG mechanism. We show that if all players use the bb strategy and update each round, bb converges when the number of slots is at most 2, but does not always converge for 3 or more slots. On the other hand, we present a simple variant which is guaranteed to converge to the same fixed point for any number of slots. In a model in which only one randomly chosen player updates each round according to the bb strategy, we prove that convergence occurs with probability 1. We complement our theoretical results with empirical studies. 1.

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Abstract. Sponsored search involves running an auction among advertisers who bid in order to have their ad shown next to search results for specific keywords. The most popular auction for sponsored search is the “Generalized Second Price ” (GSP) auction where advertisers are assigned to slots in the decreasing order of their score, which is defined as the product of their bid and click-through rate. One of the main advantages of this simple ranking is that bidding strategy is intuitive: to move up to a more prominent slot on the results page, bid more. This makes it simple for advertisers to strategize. However this ranking only maximizes efficiency under the assumption that the probability of a user clicking on an ad is independent of the other ads shown on the page. We study a Markovian user model that does not make this assumption. Under this model, the most efficient assignment is no longer a simple ranking function as in GSP. We show that the optimal assignment can be found efficiently (even in near-linear time). As a result of the more sophisticated structure of the optimal assignment, bidding dynamics become more complex: indeed it is no longer clear that bidding more moves one higher on the page. Our main technical result is that despite the added complexity of the bidding dynamics, the optimal assignment has the property that ad position is still monotone in bid. Thus even in this richer user model, our mechanism retains the core bidding dynamics of the GSP auction that make it useful for advertisers. 1

Abstract. One of the most important yet insufficiently studied issues in online advertising is the externality effect among ads: the value of an ad impression on a page is affected not just by the location that the ad is placed in, but also by the set of other ads displayed on the page. For instance, a high quality competing ad can detract users from another ad, while a low quality ad could cause the viewer to abandon the page altogether. In this paper, we propose and analyze a model for externalities in sponsored search ads. Our model is based on the assumption that users will visually scan the list of ads from the top to the bottom. After each ad, they make independent random decisions with ad-specific probabilities on whether to continue scanning. We then generalize the model in two ways: allowing for multiple separate blocks of ads, and allowing click probabilities to explicitly depend on ad positions as well. For the most basic model, we present a polynomial-time incentive-compatible auction mechanism for allocating and pricing ad slots. For the generalizations, we give approximation algorithms for the allocation of ads. 1

We consider the problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit. The goal is to maximize the revenue generated by these keyword sales, bearing in mind that, as some bidders may eventually exceed their budget, not all keywords should be sold to the highest bidder. We assume that the sequence of keywords (or equivalently, of bids) is revealed on-line. Our concern will be the competitive ratio for this problem versus the off-line optimum. We extend the current literature on this problem by considering the setting where the keywords arrive in a random order. In this setting we are able to achieve a competitive ratio of 1 − ɛ under some mild, but necessary, assumptions.

We consider the budget-constrained bidding optimization problem for sponsored search auctions, and model it as an online (multiple-choice) knapsack problem. We design both deterministic and randomized algorithms for the online (multiple-choice) knapsack problems achieving a provably optimal competitive ratio. This translates back to fully automatic bidding strategies maximizing either profit or revenue for the budget-constrained advertiser. To maximize revenue from sponsored search advertising, our bidding strategy can be oblivious (i.e., without knowledge) of other bidders ’ prices and/or clickthrough-rates for those positions. We evaluate our bidding algorithms using both synthetic data and real bidding data gathered manually, and also discuss a sniping heuristic that strictly improves bidding performance. With sniping and parameter tuning enabled, our bidding algorithms can achieve a performance ratio above 90 % against the optimum by the omniscient bidder. 1.

We present the design of a banner advertising auction which is considerably more expressive than current designs. We describe a general model of expressive ad contracts/bidding and an allocation model that can be executed in real time through the assignment of fractions of relevant ad channels to specific advertiser contracts. The uncertainty in channel supply and demand is addressed by the formulation of a stochastic combinatorial optimization problem for channel allocation that is rerun periodically. We solve this in two different ways: fast deterministic optimization with respect to expectations; and a novel online sample-based stochastic optimization method— that can be applied to continuous decision spaces—which exploits the deterministic optimization as a black box. Experiments demonstrate the importance of expressive bidding and the value of stochastic optimization. 1

We examine a formal model of sponsored search in which advertisers can bid not only on search terms, but on search terms under specific contexts. A context is any auxiliary information that might accompany a search, and might include information that is factual, estimated or inferred. Natural examples of contexts include the zip code, gender, or abstract “intentions ” (such as researching a vacation) of the searcher. After introducing a natural probabilistic model for context-based auctions, we prove several theoretical results, including the fact that under rather general circumstances, the overall social welfare of the advertisers and auctioneer together can only increase when moving from standard to context-based mechanisms. In contrast, we also provide and discuss specific examples in which only one party (advertisers or auctioneer) benefit at the expense of the other in moving to context-based search, and we give extensive simulations contrasting standard and context-based mechanisms in light of these observations.

We present a practical system for conducting sealed-bid auctions that preserves the secrecy of the bids while providing for verifiable correctness and trustworthiness of the auction. The auctioneer must accept all bids submitted and follow the published rules of the auction. No party receives any useful information about bids before the auction closes and no bidder is able to change or repudiate her 1 bid. Our solution uses Paillier’s homomorphic encryption scheme [25] for zero knowledge proofs of correctness. Only minimal cryptographic technology is required of bidders; instead of employing complex interactive protocols or multi-party computation, the single auctioneer computes optimal auction results and publishes proofs of the results ’ correctness. Any party can check these proofs of correctness via publicly verifiable computations on encrypted bids. The system is illustrated through application to firstprice, uniform-price and second-price auctions, including multiitem auctions. Our empirical results demonstrate the practicality of our method: auctions with hundreds of bidders are within reach of a single PC, while a modest distributed computing network can accommodate auctions with thousands of bids. 1.

Abstract. We analyze symmetric pure strategy equilibria in dynamic sponsored search auction games using simulations, restricting the strategies to several in a class of greedy bidding strategies introduced by Cary et al. We show that a particular convergent strategy, “balanced bidding”, also exhibits high stability to deviations in the dynamic setting. On the other hand, a cooperative strategy which yields high payoffs to all players is not sustainable in equilibrium play. Additionally, we analyze a repeated game in which each stage is a static complete-information sponsored search game. In this setting, we demonstrate a collusion strategy which yields high payoffs to all players and empirically show it to be sustainable over a range of settings. Finally, we show how a collusive strategy profile can arise even in the case of incomplete information. 1