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Essays in Auction Theory Centerç CentERç EmiEl maasland Essays in auction Theory Essays in Auction Theory Essays in Auction Theory Proefschrift ter verkrijging van de graad van doctor aan Tilburg University op gezag van de rector magnificus, prof. dr. Ph. Eijlander, in het openbaar te verdedigen ten overstaan van een door het college voor promoties aangewezen commissie in de aula van de Universiteit op vrijdag 24 februari 2012 om 12.15 uur door Emiel Maasland geboren op 5 december 1970 te Rotterdam Promotiecommissie Promotores: prof. dr. E.E.C. van Damme prof. dr. M.C.W. Janssen Overige leden: prof. dr. J. Boone prof. dr. M.F.M. Canoy prof. dr. J.K. Goeree prof. dr. T.J.S. Offerman prof. dr. J.J.M. Potters Acknowledgements This thesis is the result of my work at the CentER for Economic Research at Tilburg Uni- versity (1996-2000) and the Erasmus University Rotterdam (2001-present). CentER, with its large number of faculty and Ph.D. students, frequent seminars and numerous world-renowned visitors, is truly an excellent place for study and research. During my Ph.D. years in Tilburg, I had ample opportunities to visit interesting workshops and conferences abroad, enabling me to meet the key auction experts and game theorists in the world. CentER is greatly acknowl- edged for the financial support. As of 2001, I started to work as a researcher for SEOR, an applied economic research institute that operates independently under the umbrella of the Erasmus University Rotterdam as part of the Erasmus School of Economics. I am grateful to SEOR for giving me the opportunity to finalize my Ph.D. thesis within precious SEOR time. Without the guidance and the help of many individuals, this thesis would not have had the quality that it has now. I would like to express my sincere gratitude to all of them for helping me and inspiring me. First and foremost, my utmost gratitude goes to my promoters Eric van Damme and Maarten Janssen. I thank Eric, besides encouraging me to do the NAKE program and to visit workshops and conferences, for his intellectual guidance of my research, not only in my Tilburg years but also after I had moved to Rotterdam. I also like to thank Eric for involving me in several interesting consulting projects. Working on these projects made me realize that my main added value is to translate theoretical insights into practical policy recommendations. I thank Maarten (who also was my Master’s thesis supervisor at the Erasmus University Rotterdam) for encouraging me to start writing a dissertation, and for recommending me to Eric back in 1996. I am also thankful for his moral and intellectual support after I had returned to Rotterdam in 2001, and for co-authoring two chapters of this thesis. Maarten has been very influential in my academic career to date. I would like to express my gratitude to the members of the thesis committee, Jan Boone, Marcel Canoy, Jacob Goeree, Theo Offerman, and Jan Potters, for reading the manuscript. It is an honor to have them on my committee. I am also grateful to my co-authors Sander Onderstal (Chapters 1-3), Jacob Goeree (Chap- ter 3), John Turner (Chapter 3), Maarten Janssen (Chapters 4 and 5), Vladimir Karamychev (Chapters 4 and 5). It was a pleasure to work with each of them. Thanks to them the chapters iii iv Acknowledgements in this thesis have made it to publication in international top journals. I am also indebted to Paul Klemperer. Thanks to his inspiring lectures on the economics of auctions during the NAKE workshop in Maastricht in my first week as Ph.D. student my interest for auction theory had been triggered. This, together with the fact that auctions were reallyahottopicatthattime(governmentsallovertheworldstruggledwiththequestion whether or not to use auctions to allocate scarce resources and how to design auctions once chosen for auctions), made a decision to start writing a thesis on auction theory not hard to make. I have greatly benefited from discussions with Paul on real-life auctions, in particular the UMTS auctions in Europe. I also like to thank my fellow Ph.D. students at CentER and my colleagues at SEOR for the enjoyable discussions we had. Special thanks to my paranymphs Sander Onderstal and Ewa Mendys-Kamphorst. Sander was my office mate in Tilburg, Ewa in Rotterdam. Sander and Ewa have become true friends along the way. Finally, I would like to thank my parents for their unflagging support throughout. To them I dedicate this thesis. Rotterdam, August 2011 Contents Acknowledgements iii 1 A Swift Tour of Auction Theory and its Applications 1 1.1Introduction...................................... 1 1.2Single-ObjectAuctions................................ 4 1.2.1 TheSIPVModel............................... 5 1.2.2 EquilibriumBiddingintheSIPVModel.................. 5 1.2.3 RevenueEquivalenceandOptimalAuctions................ 11 1.2.4 RelaxingtheSIPVModelAssumptions.................. 14 1.2.5 Summary................................... 18 1.3AuctioningIncentiveContracts........................... 19 1.3.1 TheModel.................................. 20 1.3.2 TheOptimalMechanism.......................... 21 1.3.3 Summary................................... 22 1.4Multi-ObjectAuctions................................ 23 1.4.1 Auctions of Multiple Identical Objects with Single-Object Demand . 24 1.4.2 Auctions of Multiple Non-Identical Objects with Single-Object Demand 26 1.4.3 Auctions of Multiple Identical Objects with Multi-Object Demand . 27 1.4.4 Auctions of Multiple Non-Identical Objects with Multi-Object Demand 31 1.4.5 Summary................................... 37 1.5Conclusions...................................... 37 1.5.1 OutlineoftheThesis............................. 38 1.6Appendix:Proofs................................... 39 1.7References....................................... 48 2 Auctions with Financial Externalities 57 2.1Introduction...................................... 57 2.1.1 RelatedLiterature.............................. 59 2.2TheModel...................................... 61 2.3ZeroReservePrice.................................. 62 v vi CONTENTS 2.3.1 First-PriceSealed-BidAuction....................... 63 2.3.2 Second-PriceSealed-BidAuction...................... 64 2.3.3 RevenueComparison............................. 66 2.4PositiveReservePrice................................ 66 2.4.1 First-PriceSealed-BidAuction....................... 67 2.4.2 Second-PriceSealed-BidAuction...................... 69 2.5ConcludingRemarks................................. 72 2.6Appendix:Proofs................................... 73 2.7References....................................... 83 3How(Not)toRaiseMoney 85 3.1Introduction...................................... 85 3.2Winner-PayAuctions................................ 87 3.3All-PayAuctions................................... 90 3.4 Optimal Fund-Raising Mechanisms . 93 3.5Conclusion...................................... 95 3.6Appendix:Proofs................................... 97 3.7References.......................................105 4 Simultaneous Pooled Auctions with Multiple Bids and Preference Lists 109 4.1Introduction......................................109 4.2TheModel......................................112 4.3Analysis........................................114 4.4ConcludingRemarks.................................122 4.5References.......................................123 5 Auctions with Flexible Entry Fees 125 5.1Introduction......................................125 5.2TheBasicModel...................................128 5.3TheGeneralModelwithIndependentTypes....................134 5.4CorrelatedTypes...................................137 5.5DiscussionandConclusion..............................139 5.6Appendix:Proofs...................................141 5.7References.......................................148 Summary 151 Chapter 1 A Swift Tour of Auction Theory and its Applications 1.1 Introduction In the past few decades, auction theory has become one of the most active research areas in economic sciences. The focus on auctions is not surprising, as auctions have been widely used over thousands of years to sell a remarkable range of commodities. One of the earliest reports of an auction is by the old Greek historian Herodotus of Halicarnassus, who writes about men in Babylonia around 500 B.C bidding for women to become their wives.1 Perhaps the most astonishing auction in history took place in 193 A.D. when the Praetorian Guard put the entire Roman Empire up for auction. Didius Julianus was the highest bidder. However, he fell prey to what, today, is known as the winner’s curse: he was beheaded two months later when Septimus Severus conquered Rome.2 Nowadays, the use of auctions is widespread. There are auctions for perishable goods such as cattle, fish, and flowers; for durables including art, real estate, and wine; and for abstract objects like treasury bills, licenses for “third generation” (3G) mobile telecommunication (or UMTS), and electricity distribution contracts.3 In some of these auctions, the amount of money raised is almost beyond imagination. In the 1990s, the US government collected tens of billions of dollars from auctions for licenses for second generation mobile telecommunications,4 and in 2000, the British and German governments, together, raised almost 100 billion euros 1 Some have called Herodotus the Father of History, while others have called him the Father of Lies (Pipes, 1998-1999). There may be some doubt, therefore, about whether auctions for women really took place. 2 These, and other examples of remarkable auctions, can be found in
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