DESIGN AND ANALYSIS OF SPONSORED SEARCH MECHANISMS A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Renato Paes Leme December 2012 c 2012 Renato Paes Leme ALL RIGHTS RESERVED DESIGN AND ANALYSIS OF SPONSORED SEARCH MECHANISMS Renato Paes Leme, Ph.D. Cornell University 2012 Auctions have become the standard way of allocating resources in electronic markets. Two main reasons why designing auctions is hard are the need to cope with strategic behavior of the agents, who will constantly adjust their bids seeking more items at lower prices, and the fact that the environment is highly dynamic and uncertain. Many market designs which became de-facto industrial standards allow strategic manipulation by the agents, but nevertheless display good behavior in practice. In this thesis, we analyze why such designs turned out to be so successful despite strategic behavior and environment uncertainty. Our goal is to learn from this analysis and to use the lessons learned to design new auction mechanisms; as well as fine-tune the existing ones. We illustrate this research line through the analysis and design of Ad Auc- tions mechanisms. We do so by studying the equilibrium behavior of a game induced by Ad Auctions, and show that all equilibria have good welfare and revenue properties. Next, we present new Ad Auction designs that take into ac- count richer features such as budgets, multiple keywords, heterogeneous slots and online supply. BIOGRAPHICAL SKETCH Renato Paes Leme was born in December 1st, 1984 in Rio de Janeiro, where he spent most of his life. There in the tropics, he got a BEng in Computer Engi- neering from Instituto Militar de Engenharia in 2007 and a MSc in Mathematics from Instituto Nacional de Matematica Pura e Aplicada in the same year. He then moved to Ithaca (not quite in the tropics, but beautiful nevertheless) where he expects to get a PhD in Computer Science with a minor in Operations Re- search from Cornell University in December 2012. iii I dedicate this thesis to my parents Irio and Sylvia and to my brother Pedro. iv ACKNOWLEDGEMENTS I want thank Eva´ Tardos for guiding me through this amazing journey that was my PhD education. Eva´ was the main force shaping my view of science and my taste for research problems. The researcher I am today, I owe to her. What I’ll miss more about Cornell will undoubtely be the conversations I had with her. I remember countless visits to her office when Eva´ was always patient and took time to walk with me over many angles of the question - technical and non- technical. Above all, I thank her for the care and attention she had for me in the past four years. I am lucky to have been at such a wonderful place as Cornell, where I found many great mentors, who were sources of inspiration and example for me. I’d like to thank David Shmoys for suggesting interesting problems and for teach- ing me a lot about linear programming and scheduling. Also, thanks David for being my co-advisor and for being always a great source of advice. Many thanks to Bobby Kleinberg for being a great mentor, a great inspiration and for always being able to hint me in the right direction. I am grateful to Jon Klein- berg for his “Structure of Information Networks” class, which was the first class I took at Cornell and filled my mind with all sorts of interesting questions to think about. To David Williamson for his “Approximation Algorithms” class from which I learned a great deal of useful techniques that I later applied in my research. Thanks to Emin G ¨un Sirer for serving on my committee and for general advice. To many others faculty members that I had the pleasure to be in contact with during my PhD years, many thanks. I was very fortunate to be able to spend some part of my PhD years travelling and visiting various institutions and research labs. A special thanks for my industry mentors Moshe Babaioff (who hosted me for a semester in Microsoft v Research Sillicon Valley), Jennifer Chayes and Christian Borgs (for hosting me in Microsoft Research New England for one summer and then for many following visits) and Vahab Mirrokni (for hosting me in Google NYC for two summers and countless many visits during the semester). I was also fortunate to spend two months in the Institute of Advanced Studies in the Hebrew University of Jerusalem (thanks to Noam Nisan and Michal Feldman for organizing the AGT semester, bringing together all the great AGT researchers to the same place and creating such a stimulating research environment). I also had the pleasure to visit MIT-CSAIL for one semester (thanks to Silvio Micali and Costis Daskalakis for hosting me). I made several friends among my research collaborators, and I’d like to thank them all for all the fun moments doing research together. In special, I’ll like to thank Vasilis Syrgkanis for being a great friend and such a fun research collaborator. I specially remember solving the main question in our SODA pa- per while on the beach in Netanya and the many times we discussed game the- ory while eating shakshouka for breakfast in Jerusalem. Thanks also to Brendan Lucier for a very fruitful collaboration on GSP auc- tions and for teaching me many interesting techniques. Thanks to Gagan Goel with whom I learned a lot about truthful auctions and submodular functions and teaching me how to appreciate NYC (in particular showing me where to get good southern Indian food). One other gift I got from Cornell is many good friends who made my life here fun and interesting. They formed an important part of my PhD: Bruno Abrahao, Daniel Hauagge, Guilherme Pinto, Hussam Abu-Libdeh, Ashwin Baranidyuru, Daniel Fleischman, Shahar Dobzinski, Sigal Oren, Georgios Pil- iouras and Marcos Salles. vi A special thanks to my friends Thiago Pereira and Thiago Costa for being my great friends for a very long time, since we were all undergrads in Brazil. They both shared with me moments during our undergrad and masters and the anxiety applying for a PhD. We went together through moments of the happi- ness and dispair in our doctoral studies and sharing them along the way was very important to me. I thank Thiago Costa and Andrei Roman for making my year in Boston so fun and for providing me warmth with your friendship. I also thank Thiago Pereira for introducing me to the ICPC contest during our under- grad years, which was my initial contact with algorithms. It was very fun to spend many nights programming with him and Rafael Paulino. Thiago Pereira should also get the credit for introducing me to travelling - thanks for many interesting trips we had through Europe. I want to thank my friends from Brazil: Rodrigo, Alexandre, Nathalia, Cechin and Nicodemos. There are many great things that happened while I was in Boston, but noth- ing compared to meeting my dear Carol. Thanks for all the beautiful moments we had since then and for always inspiring me in my research and beyond. Thanks for filling my life with joy. Above all, I’d like to thank my parents Irio and Sylvia, who always loved me and supported me in all my decisions. They taught me to be persistent and never give up on problems, which was definitely very useful in research and in life overall. The love of my parents, my brother Pedro and all my family have been my constant support all this years. To you I dedicate this thesis. vii TABLE OF CONTENTS BiographicalSketch.............................. iii Dedication ................................... iv Acknowledgements.............................. v TableofContents ............................... viii ListofTables.................................. xi ListofFigures ................................. xii 1 Introduction 1 1.1 Comparing Algorithms in Strategic Settings (or Mechanism Design for Algorithmists) . 2 1.2 TheMainInquiryofthisThesis . 4 1.3 AnalysisApproachtoSponsoredSearch . 8 1.3.1 SponsoredSearchAuctionsandGSP. 8 1.3.2 SocialWelfare .......................... 12 1.3.3 Robustness ........................... 13 1.3.4 Revenue ............................. 15 1.3.5 Relatedwork .......................... 17 1.4 DesigningSponsoredSearchMechanisms . 18 1.4.1 BudgetConstraints. 19 1.4.2 OnlineSupply.......................... 22 1.4.3 RelatedWork .......................... 25 1.5 Roadmap................................. 28 1.6 BibliographicNotes. .. .. .. .. .. .. .. 29 2 Technical Preliminaries 31 2.1 BasicNotation.............................. 31 2.2 MechanismDesignBasics . 32 2.3 SolutionConcepts............................ 33 2.4 BayesianSolutionConcepts . 36 2.5 PriceofAnarchyandRevenue . 38 2.6 VCG Mechanism: a generic welfare-maximizing mechanism ... 39 2.7 SponsoredSearchEnvironment . 41 2.7.1 Single-keywordenvironment . 41 2.7.2 GeometricRepresentation . 42 2.7.3 Multi-keywordenvironment . 43 2.8 PolyhedralandPolymatroidalEnvironments . .. 44 2.8.1 Sponsored Search as a Polymatroidal Environment . 45 2.8.2 Qualityfactors ......................... 47 2.9 GeneralizedSecondPriceAuction . 48 2.9.1 Nooverbidding......................... 49 viii 3 Efficiency of Equilibria in GSP 51 3.1 PriceofStability............................. 51 3.2 PriceofAnarchywithUncertainty . 59 3.3 Pure Nash Equilibria in the Full Information Setting . ..... 65 3.3.1 Weaklyfeasibleallocations . 65 3.3.2 TwoandThreeslotscase. 67 3.3.3 GoldenRatioUpperBoundforthePriceofAnarchy. 70 3.4 Computational search for the GSP Price of Anarchy . .. 73 3.5 QualityofLearningOutcomesinGSP . 76 3.5.1 Learninginthefullinformationsetting . 76 3.5.2 Learningwithuncertainty. 78 4 Revenue of Equilibria in GSP 80 4.1 RevenuewithUncertainty . 81 4.1.1 Usefulsetoftools. .. .. .. .. .. .. 82 4.1.2 RevenuewithoutReserves:BadExamples . 83 4.1.3 Warmup:MHRValuations . 84 4.1.4 Regularvaluations . 86 4.1.5 BayesianRevenuewithWell-separatedCTRs . 89 4.2 RevenueinFullInformationGSP . 93 4.2.1 FullInformationRevenue:Examples . 94 4.2.2 RevenueBoundinFullInformation . 94 4.3 TradeoffbetweenRevenueandEfficiency . 99 4.3.1 EquilibriumhierarchyforGSP . 100 4.3.2 Envy-freeandefficientequilibrium . 101 4.3.3 Costofefficiency:definitionandexample .