Auctions with variable supply and competing auctioneers [Elektronische Ressource] / vorgelegt von Damian Stefanov Damianov

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• Publié par: ruprecht-karls-universitat_heidelberg
• Publié le: 01 janvier 2006
• Nombre de lectures: 25
• Langue: English

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Auctions with Variable Supply
and Competing Auctioneers
Dissertation
zur Erlangung des akademschen Grades
Doctor Rerum Politicarum
an der
˜ ˜Fakultat fur Wirtschafts- und Sozialwissenschaften
˜der Ruprecht-Karls-Universitat Heidelberg
vorgelegt von
Damian Stefanov Damianov
geboren in Sofia, Bulgarien
Heidelberg, Juli 2005Acknowledgements
This dissertation originated due to the guidance, encouragement and support of many
people, and I would like to take here the opportunity to thank all of them. First of all,
I would like to express my heartfelt gratitude and intellectual debt to my supervisor,
Jurgen˜ Eichberger. He guided my research throughout all the stages of this long-term
project and taught me how to separate the interesting from the trivial, the essential
from the unimportant. At the same time he gave me the freedom to choose a research
topic and develop my own ideas. His in uence on my development as an economist
and researcher is substantial. I am also very grateful to J˜org Oechssler for his valuable
guidance and helpful advice. He kindly agreed to act as a second advisor.
This thesis beneflted a lot from the discussions with Switgard Feuerstein and Hans
Gersbach. They read parts of this work and made constructive suggestions. I would
also like to thank Hans Haller for the illuminating discussions during his visits at the
University of Heidelberg. He made constructive comments to all chapters. I too am
verygratefultomycolleagueandcollaboratorJohannesGerdBecker,whoco-authored
twopapers,onwhichtheexpositioninchapter3isbased. Workingwithhimwasforme
bothanenjoyableandvaluableexperience. IwouldlikealsotothankAniGuerdjikova,
DmitriVinogradov,AlexanderZimper,aswellasmyothercolleaguesattheUniversity
of Heidelberg. All of them provided valuable comments during the research seminars
at the University of Heidelberg and in personal discussions. I am also grateful to Ute
Schumacher, who is always very forthcoming and friendly.
The Alfred-Weber Institute of the University of Heidelberg, the Germany Research
Foundation(DFG)andtheGermanEconomicAssociation(VSP)providedmanytrav-
elling grants, which enabled my participation at a number of international confer-
ences. These events were an invaluable opportunity for me to exchange ideas and
discuss my results with many international researchers. I am grateful for the help-
ful advice of Roberto Burguet, Jurgen˜ Bierbaum, Dirk Engelmann, Veronika Grimm,
Angel Hernando-Veciana, Radosveta Ivanova-Stenzel, Dan Kovenock, Yvan Lengwiler,
Giuseppe Lopomo, Preston McAfee, David Reiley, Mike Shor, Jens Tapking, Thomas
Tr˜oger and Charles Zheng.
th thThanks are also due to the participants of the 58 and 59 European Meetings of the
Econometric Society in Stockholm 2003 and Madrid 2004, as well as the 2005 North
American Winter Meeting of Econometric Society in Philadelphia. I am grateful also
th thto the participants of the 9 and 10 Spring Meetings of Young Economists, which
took place in Warsaw 2004 and in Geneva 2005, as well as to the participants of
iiththe 19 Annual Congress of the European Economic Association in Madrid 2004,
the International Industrial Organization Conference in Atlanta, 2005 and the 2005
Conference of the Society for the Advancement in Economic Theory in Vigo.
I am also very indebted to Elmar Wolfstetter for inviting me to give a talk in the
research seminar at the Humboldt University, Berlin in 2002, Wolfgang Leininger for
his invitation for a presentation at the University of Dortmund in 2004, Erwin Amann
for inviting me tot a paper at the University of Essen-Duisburg in 2005, and
Roberto Burguet for inviting me to attend the Barcelona Economics Workshop on
Auction Markets in 2005. All these people were very generous to me. Without their
help this thesis wouldn’t have existed (at least not in this form).
Many thanks of another kind go to my wife Ekaterina and my son Peter for their love
and their unconditional support for this undertaking. My wife was always willing to
discuss the topic with me. She proofread carefully and improved the style of all the
papers I wrote. I am indebted to my parents-in-law for their help and moral support
as well.
Finally,IwouldliketoexpressmydeepestgratitudetomyparentsVelichkaandStefan,
who always fostered my desire to study.
Heidelberg, July 2005
iiiContents
1 Introduction 1
1.1 Purpose of the thesis and approach . . . . . . . . . . . . . . . . . . . . 4
1.2 Overview of the thesis and results . . . . . . . . . . . . . . . . . . . . . 5
2 Multi-Unit Auctions with Variable Supply: Applications 7
2.1 Treasury auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Initial Public Ofierings (IPOs) . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Other applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 CommonValueAuctionswithVariableSupply: UniformPriceversus
Discriminatory 12
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 Related theoretical literature . . . . . . . . . . . . . . . . . . . . 13
3.1.2 Nash equilibria and rationalizable strategies . . . . . . . . . . . 14
3.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.2 Auction games . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2.1 Pure strategies . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2.2 Mixed . . . . . . . . . . . . . . . . . . . . . 18
3.3 Deflnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 The uniform price and the discriminatory auctions . . . . . . . . . . . . 20
3.4.1 Payofis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4.2 Discriminatory auction (D) . . . . . . . . . . . . . . . . . . . . 21
3.4.3 Uniform price auction (U) . . . . . . . . . . . . . . . . . . . . . 23
3.4.3.1 The two bidder case . . . . . . . . . . . . . . . . . . . 23
3.4.3.2 The general case . . . . . . . . . . . . . . . . . . . . . 28
ivContents
3.4.4 Revenue and average trade volume . . . . . . . . . . . . . . . . 32
3.4.4.1 Revenue . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.4.2 Average trade volume . . . . . . . . . . . . . . . . . . 33
3.4.5 A numerical example . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Appendix 3.A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Appendix 3.B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Static and Dynamic Auctions with Variable Supply 49
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.1 Relation to the theoretical literature . . . . . . . . . . . . . . . 50
4.1.2 Organization of the chapter . . . . . . . . . . . . . . . . . . . . 51
4.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1 The setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.2 Trade mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.3 Procedures for collecting bids . . . . . . . . . . . . . . . . . . . 52
4.2.4 Pricing rules: uniform price (U) and discriminatory (D) . . . . . 53
4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.1 The second stage of the game . . . . . . . . . . . . . . . . . . . 54
4.3.2 Uniform pricing (U) . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.2.1 Simultaneous and sequential collection of bids . . . . . 57
4.3.2.2 Ascending clock auction . . . . . . . . . . . . . . . . . 60
4.3.2.3 Descending clock auction . . . . . . . . . . . . . . . . 64
4.3.3 Discriminatory pricing (D) . . . . . . . . . . . . . . . . . . . . . 69
4.4 Revenues, average trade volume and e–ciency . . . . . . . . . . . . . . 70
4.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Appendix 4.A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Auctions with Variable Supply and the Walrasian Outcome 80
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.1.1 Relation to monopoly price discrimination . . . . . . . . . . . . 81
5.1.2 to the literature on competitive market games . . . . . 83
5.1.3 Organization of the chapter . . . . . . . . . . . . . . . . . . . . 84
vContents
5.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.2 The competitive equilibrium . . . . . . . . . . . . . . . . . . . . 85
5.2.3 Two-stage mechanisms . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.4 Variable supply auctions . . . . . . . . . . . . . . . . . . . . . . 88
5.2.4.1 The stopout price. . . . . . . . . . . . . . . . . . . . . 88
5.2.4.2 Rationing rules . . . . . . . . . . . . . . . . . . . . . . 89
5.2.4.3 Pricing rules . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3.1 The main result . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.2 The uniform price auction . . . . . . . . . . . . . . . . . . . . . 101
5.3.2.1 Exampleoflow-priceequilibriumwiththe\