An Adaptive Sponsored Search Mechanism δ-Gain Truthful in Valuation, Time, and Budget

This paper presents an online sponsored search auc-tion that motivates advertisers to report their true budget, arrival time, departure time, and value per click.The auction is based on a modified Multi-Armed Ban-dit (MAB) mechanism that allows for advertisers whoarrive and depart in an online fashion, have a value perclick, and are budget constrained.In tackling the problem of truthful budget, arrivaland departure times, it turns out that it is not possi-ble to achieve truthfulness in the classical sense (whichwe show in a companion paper). As such, we definea new concept called δ-gain. δ-gain bounds the util-ity a player can gain by lying as opposed to his utilitywhen telling the truth. Building on the δ-gain conceptwe define another new concept called relative 2-gain,which bounds the relative ratio of the gain a player canachieve by lying with respect to his true utility. Weargue that for many practical applications if the δ-gainand or the relative 2-gain are small, then players willnot invest time and effort in making strategic choicesbut will truthtell as a default strategy. These conceptscapture the essence of dominant strategy mechanismsas they lead the advertiser to choose truthtelling overother strategies.In order to achieve δ-gain truthful mechanism this paper also presents a new payment scheme, Time se-ries Truthful Payment Scheme (TTPS), for an onlinebudget-constrained auction mechanism. The paymentscheme is a generalization of the VCG principles for anonline scheduling environment with budgeted players.Using the concepts of δ-gain truthful we presentthe only known budget-constrained sponsored searchauction with truthful guarantees on budget, arrivals,departures, and valuations. Previous works that deal ∗Yahoo! Research Labs, 701 First Street, Sunnyvale, CA 94089. Email: [email protected] We are submitting this paper for confidential review, all rights reserved†E15-313 Media Lab, MIT, Cambridge MA, 02149. Email: [email protected] advertiser budgets only deal with the non-strategiccase.