We consider the "Offline Ad Slot Scheduling" problem, where advertisers must be scheduled to "sponsored search" slots during a given period of time. Advertisers specify a budget constraint, as well as a maximum cost per click, and may not be assigned to more than one slot for a particular search. We give a truthful mechanism under the utility model where bidders try to maximize their clicks, subject to their personal constraints. In addition, we show that the revenue-maximizing mechanism is not truthful, but has a Nash equilibrium whose outcome is identical to our mechanism. As far as we can tell, this is the first treatment of sponsored search that directly incorporates both multiple slots and budget constraints into an analysis of incentives. Our mechanism employs a descending-price auction that maintains a solution to a certain machine scheduling problem whose job lengths depend on the price, and hence is variable over the auction. The price stops when the set of bidders that can afford that price pack exactly into a block of ad slots, at which point the mechanism allocates that block and continues on the remaining slots. To prove our result on the equilibrium of the revenue-maximizing mechanism, we first show that a greedy algorithm suffices to solve the revenue-maximizing linear program; we then use this insight to prove that bidders allocated in the same block of our mechanism have no incentive to deviate from bidding the fixed price of that block.
There is some work on algorithms for allocating bidders with budgets to keywords that arrive online, where the bidders place (possibly different) bids on particular keywords @cite_11 @cite_16 . The application of this work is similar to ours, but their concern is purely online optimization; they do not consider the game-theoretic aspects of the allocation. @cite_3 derive a linear program for the offline optimization problem of allocating bidders to queries, and handle multiple positions by using variables for slates'' of bidders. Their LP is related to ours, but again they do not consider game-theoretic aspects of their proposed allocations.
@cite_16 @cite_3 @cite_11
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We study an online assignment problem, motivated by Adwords Allocation, in which queries are to be assigned to bidders with budget constraints. We analyze the performance of the Greedy algorithm (which assigns each query to the highest bidder) in a randomized input model with queries arriving in a random permutation. Our main result is a tight analysis of Greedy in this model showing that it has a competitive ratio of 1 - 1 e for maximizing the value of the assignment. We also consider the more standard i.i.d. model of input, and show that our analysis holds there as well. This is to be contrasted with the worst case analysis of [MSVV05] which shows that Greedy has a ratio of 1 2, and that the optimal algorithm presented there has a ratio of 1 - 1 e. The analysis of Greedy is important in the Adwords setting because it is the natural allocation algorithm for an auction-style process. From a theoretical perspective, our result simplifies and generalizes the classic algorithm of Karp, Vazirani and Vazirani for online bipartite matching. Our results include a new proof to show that the Ranking alforithm of [KVV90] has a ratio of 1 - 1 e in the worst case. It has been recently discovered [KV07] (independent of our results) that one of the crucial lemmas in [KVV90], related to a certain reduction, is incorrect. Our proof is direct, in that it does not go via such a reduction, which also enables us to generalize the analysis to our online assignment problem. We describe a real-time bidding algorithm for performance-based display ad allocation. A central issue in performance display advertising is matching campaigns to ad impressions, which can be formulated as a constrained optimization problem that maximizes revenue subject to constraints such as budget limits and inventory availability. The current practice is to solve the optimization problem offline at a tractable level of impression granularity (e.g., the page level), and to serve ads online based on the precomputed static delivery scheme. Although this offline approach takes a global view to achieve optimality, it fails to scale to ad allocation at the individual impression level. Therefore, we propose a real-time bidding algorithm that enables fine-grained impression valuation (e.g., targeting users with real-time conversion data), and adjusts value-based bids according to real-time constraint snapshots (e.g., budget consumption levels). Theoretically, we show that under a linear programming (LP) primal-dual formulation, the simple real-time bidding algorithm is indeed an online solver to the original primal problem by taking the optimal solution to the dual problem as input. In other words, the online algorithm guarantees the offline optimality given the same level of knowledge an offline optimization would have. Empirically, we develop and experiment with two real-time bid adjustment approaches to adapting to the non-stationary nature of the marketplace: one adjusts bids against real-time constraint satisfaction levels using control-theoretic methods, and the other adjusts bids also based on the statistically modeled historical bidding landscape. Finally, we show experimental results with real-world ad delivery data that support our theoretical conclusions. This paper is concerned with the joint allocation of bid price and campaign budget in sponsored search. In this application, an advertiser can create a number of campaigns and set a budget for each of them. In a campaign, he she can further create several ad groups with bid keywords and bid prices. Data analysis shows that many advertisers are dealing with a very large number of campaigns, bid keywords, and bid prices at the same time, which poses a great challenge to the optimality of their campaign management. As a result, the budgets of some campaigns might be too low to achieve the desired performance goals while those of some other campaigns might be wasted; the bid prices for some keywords may be too low to win competitive auctions while those of some other keywords may be unnecessarily high. In this paper, we propose a novel algorithm to automatically address this issue. In particular, we model the problem as a constrained optimization problem, which maximizes the expected advertiser revenue subject to the constraints of the total budget of the advertiser and the ranges of bid price change. By solving this optimization problem, we can obtain an optimal budget allocation plan as well as an optimal bid price setting. Our simulation results based on the sponsored search log of a commercial search engine have shown that by employing the proposed method, we can effectively improve the performances of the advertisers while at the same time we also see an increase in the revenue of the search engine. In addition, the results indicate that this method is robust to the second-order effects caused by the bid fluctuations from other advertisers. 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. Our bidding strategy for revenue maximization is oblivious (i.e., without knowledge) of other bidders' prices and or click-through-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.