## A Truthful Mechanism for Offline Ad Slot Scheduling

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Citations: | 12 - 3 self |

### BibTeX

@MISC{Feldman_atruthful,

author = {Jon Feldman and S. Muthukrishnan and Evdokia Nikolova and Martin Pál},

title = {A Truthful Mechanism for Offline Ad Slot Scheduling},

year = {}

}

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### Abstract

Abstract. 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. ⋆ This work was done while the author was visiting Google, Inc., New York, NY. 1

### Citations

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(Show Context)
Citation Context ...ut is just a set of budgets B1, . . . , Bn, and we need to allocate D clicks, with no ceiling on the per-click price. Here we apply a simple rule related to pricing schemes for network bandwidth (see =-=[16, 15]-=-): Let B = � i Bi. Now to each bidder i, allocate (Bi/B)D clicks. Set all prices the same: pi = p = B/D. The mechanism guarantees that each bidder exactly spends her budget, thus no bidder will report... |

626 | Worst-case equilibria
- Koutsoupias, Papadimitriou
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(Show Context)
Citation Context ... our setting one is tempted to apply a Fisher Market model: here m divisible goods are available to n buyers with money Bi, and uij(x) denotes i’s utility of receiving x amount of good j. It is known =-=[3, 10, 7]-=- that under certain conditions a vector of prices for goods exists such that the market clears, in that there is no surplus of goods, and all the money is spent. Furthermore, this price vector can be ... |

347 | Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords
- Edelman, Ostrovsky, et al.
- 2007
(Show Context)
Citation Context ...sored search that analyze the generalized second-price (GSP) auction, which is the auction currently in use at Google and Yahoo. The equilibria of this auction are characterized and compared with VCG =-=[9, 17, 2, 22]-=-. Here the utility function is the profit-maximizing utility where each bidder attempts to maximize her clicks × profit per click, and budget constraints are generally not treated. Borgs et al. [4] co... |

342 |
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(Show Context)
Citation Context ... our setting one is tempted to apply a Fisher Market model: here m divisible goods are available to n buyers with money Bi, and uij(x) denotes i’s utility of receiving x amount of good j. It is known =-=[3, 10, 7]-=- that under certain conditions a vector of prices for goods exists such that the market clears, in that there is no surplus of goods, and all the money is spent. Furthermore, this price vector can be ... |

308 |
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Citation Context ...e. In Section 3 we solve the budgets-only case by characterizing the allowable schedules in terms of the solution to a classical machine scheduling problem (to be precise, the problem Q | pmtn | Cmax =-=[13]-=-). The difficulty that arises is that the lengths of the jobs in the scheduling problem actually depend on the price charged. Thus, we incorporate the scheduling algorithm into a descending-price mech... |

197 | Position Auctions
- Varian
(Show Context)
Citation Context ...sored search that analyze the generalized second-price (GSP) auction, which is the auction currently in use at Google and Yahoo. The equilibria of this auction are characterized and compared with VCG =-=[9, 17, 2, 22]-=-. Here the utility function is the profit-maximizing utility where each bidder attempts to maximize her clicks × profit per click, and budget constraints are generally not treated. Borgs et al. [4] co... |

143 | Tsitsiklis. Efficiency loss in a network resource allocation game
- Johari, N
(Show Context)
Citation Context ...ut is just a set of budgets B1, . . . , Bn, and we need to allocate D clicks, with no ceiling on the per-click price. Here we apply a simple rule related to pricing schemes for network bandwidth (see =-=[16, 15]-=-): Let B = � i Bi. Now to each bidder i, allocate (Bi/B)D clicks. Set all prices the same: pi = p = B/D. The mechanism guarantees that each bidder exactly spends her budget, thus no bidder will report... |

98 | 2002): “Market equilibrium via a primal-dual-type algorithm
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(Show Context)
Citation Context ...n conditions a vector of prices for goods exists such that the market clears, in that there is no surplus of goods, and all the money is spent. Furthermore, this price vector can be found efficiently =-=[8]-=-. The natural way to apply a Fisher model to a slot auction is to regard the slots as commodities and have the utilities be in proportion to the number of clicks. However this becomes problematic beca... |

98 | Adwords and generalized on-line matching
- Mehta, Saberi, et al.
- 2005
(Show Context)
Citation Context ...petitive ratio guarantee. 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 =-=[20, 19]-=-. The application of this work is similar to ours, but their concern is purely online optimization; they do not consider the gametheoretic aspects of the allocation. Abrams et al. [1] derive a linear ... |

82 |
Consensus of subjective probabilities: the parimutuel method
- Eisenberg, Gale
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(Show Context)
Citation Context ... our setting one is tempted to apply a Fisher Market model: here m divisible goods are available to n buyers with money Bi, and uij(x) denotes i’s utility of receiving x amount of good j. It is known =-=[3, 10, 7]-=- that under certain conditions a vector of prices for goods exists such that the market clears, in that there is no surplus of goods, and all the money is spent. Furthermore, this price vector can be ... |

74 | Multi-unit auctions with budget-constrained bidders
- Borgs, Chayes, et al.
- 2005
(Show Context)
Citation Context ...ze exposure. In contrast, under the profit-maximizing utility, a weak motivation for budgets is a limit on liquidity. Also, our choice of utility function is out of analytical necessity: Borgs et al. =-=[4]-=- show that under some reasonable assumptions, truthful mechanisms are impossible under a profit-maximizing utility.sAd Slot Scheduling is not truthful, but has a Nash equilibrium (under the same utili... |

71 | An Analysis of Alternative Slot Auction Designs for Sponsored Search
- Lahaie
- 2006
(Show Context)
Citation Context ...sored search that analyze the generalized second-price (GSP) auction, which is the auction currently in use at Google and Yahoo. The equilibria of this auction are characterized and compared with VCG =-=[9, 17, 2, 22]-=-. Here the utility function is the profit-maximizing utility where each bidder attempts to maximize her clicks × profit per click, and budget constraints are generally not treated. Borgs et al. [4] co... |

49 | Greedy Bidding Strategies for Keyword Auctions
- Cary, Das, et al.
- 2007
(Show Context)
Citation Context ...ed to ours, but again they do not consider game-theoretic aspects of their proposed allocations. Bidder strategies for keyword auctions in the presence of budget constraints have also been considered =-=[11, 21, 6, 5]-=-. Generally these papers are not concerned with mechanism design, but there could be some interesting relationships between the models in these papers and the one we study here. In our setting one is ... |

44 |
A level algorithm for preemptive scheduling
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(Show Context)
Citation Context ...thm. First we give an important lemma that characterizes the conditions under which a set of bidders can be allocated to a set of slots, which turns out to be just a restatement of a classical result =-=[14]-=- from scheduling theory. Lemma 1. Suppose we would like to assign an arbitrary set {1, . . . , k} of bidders to a set of slots {1, . . . , k} with D1 > . . . > Dk. Then, a click allocation c1 ≥ ... ≥ ... |

44 | Allocating Online Advertisement Space with Unreliable Estimates
- Mahdian, Nazerzadeh, et al.
(Show Context)
Citation Context ...units are impossible. Our work is different both because of the different utility function and the generalization to multiple slots with a scheduling constraint. Using related methods, Mahdian et al. =-=[19]-=- consider an online setting where an unknown number of copies of an item arrive online, and give a truthful mechanism with a constant competitive ratio guarantee. There is some work on algorithms for ... |

44 | An adaptive algorithm for selecting profitable keywords for search-based advertising services
- Rusmevichientong, Williamson
(Show Context)
Citation Context ...ed to ours, but again they do not consider game-theoretic aspects of their proposed allocations. Bidder strategies for keyword auctions in the presence of budget constraints have also been considered =-=[11, 21, 6, 5]-=-. Generally these papers are not concerned with mechanism design, but there could be some interesting relationships between the models in these papers and the one we study here. In our setting one is ... |

33 | Budget optimization in search-based advertising auctions
- Feldman, Muthukrishnan, et al.
- 2007
(Show Context)
Citation Context ...ed to ours, but again they do not consider game-theoretic aspects of their proposed allocations. Bidder strategies for keyword auctions in the presence of budget constraints have also been considered =-=[11, 21, 6, 5]-=-. Generally these papers are not concerned with mechanism design, but there could be some interesting relationships between the models in these papers and the one we study here. In our setting one is ... |

33 |
Preemptive scheduling of uniform processor systems
- Gonzalez, Sahni
- 1978
(Show Context)
Citation Context ...etes in time maxℓ≤k{ �ℓ i=1 xi/ �ℓ i=1 si}. Thus, the conditions of the lemma are exactly the conditions under which the schedule completes in one unit of time. ⊓⊔ 5 In later work, Gonzalez and Sahni =-=[12]-=- give a faster (linear-time) algorithm.s3.2 A multiple-slot budgets-only mechanism. Our mechanism will roughly be a descending-price mechanism where we decrease the price until a prefix of budgets fit... |

28 | Optimal delivery of sponsored search advertisements subject to budget constraints
- Abrams, Mendelevitch, et al.
- 2007
(Show Context)
Citation Context ...ar keywords [20, 19]. The application of this work is similar to ours, but their concern is purely online optimization; they do not consider the gametheoretic aspects of the allocation. Abrams et al. =-=[1]-=- 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, b... |

22 |
AND RAJEEV MOTWANI: Truthful auctions for pricing search keywords
- AGGARWAL, GOEL
- 2006
(Show Context)
Citation Context |

6 |
Rakesh Vohra. Sponsored search auctions
- Lahaie, Pennock, et al.
- 2007
(Show Context)
Citation Context ...d is to allocate ads to each search independently via a generalized second price (GSP) auction, where the ads are ranked by (some function of) their bid, and placed into the slots in rank order. (See =-=[18]-=- for a survey of this area.) There are several important aspects of sponsored search not captured by the original models. Most advertisers are interested in getting many clicks throughout the day on a... |

4 |
Omid Etesami, and Mohammad Mahdian. Dynamics of bid optimization in online advertisement auctions
- Borgs, Chayes, et al.
- 2007
(Show Context)
Citation Context |