Five essays in economic theory [Elektronische Ressource] / vorgelegt von Nora Szech
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Five essays in economic theory [Elektronische Ressource] / vorgelegt von Nora Szech

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Five Essays in Economic TheoryInaugural-Dissertationzur Erlangung des Grades eines Doktorsder Wirtschafts- und Gesellschaftswissenschaftendurch dieRechts- und Staatswissenschaftliche Fakult atder Rheinischen Friedrich-Wilhelms-Universit atBonnvorgelegt vonNora Szechaus Bremen2010Dekan: Prof. Dr. Christian HillgruberErstreferent: Prof. Dr. Benny MoldovanuZweitreferent: JProf. Dr. Anja Sch ottnerTag der mundlic hen Prufung: 14.09.2010Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonn(http://hss.ulb.uni-bonn.de/diss online) elektronisch publiziert.AcknowledgmentsMany people supported me in writing this thesis, and I am grateful to all of them.First I want to thank my supervisor Benny Moldovanu for all his support and inspi-ration. I learned very much from his comments and critique, not only on my ownwork.Anja Sch ottner, the second referee of my thesis, in uenced with her topics courseespecially the rst two chapters. Her advice helped me very much.Another big thank goes to Patrick Schmitz, who advised me on almost all of myprojects and gave me a lot of valuable comments and critique.From Avner Shaked I learned a lot about game theory and its place in the world.Rani Spiegler whose work inspired Chapter 2 supported me very much. PhilippWeinschenk is the coauthor of the paper presented in Chapter 3. I enjoyed verymuch to work with him.

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Published 01 January 2010
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Five Essays in Economic Theory
Inaugural-Dissertation
zur Erlangung des Grades eines Doktors
der Wirtschafts- und Gesellschaftswissenschaften
durch die
Rechts- und Staatswissenschaftliche Fakult at
der Rheinischen Friedrich-Wilhelms-Universit at
Bonn
vorgelegt von
Nora Szech
aus Bremen
2010Dekan: Prof. Dr. Christian Hillgruber
Erstreferent: Prof. Dr. Benny Moldovanu
Zweitreferent: JProf. Dr. Anja Sch ottner
Tag der mundlic hen Prufung: 14.09.2010
Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonn
(http://hss.ulb.uni-bonn.de/diss online) elektronisch publiziert.Acknowledgments
Many people supported me in writing this thesis, and I am grateful to all of them.
First I want to thank my supervisor Benny Moldovanu for all his support and inspi-
ration. I learned very much from his comments and critique, not only on my own
work.
Anja Sch ottner, the second referee of my thesis, in uenced with her topics course
especially the rst two chapters. Her advice helped me very much.
Another big thank goes to Patrick Schmitz, who advised me on almost all of my
projects and gave me a lot of valuable comments and critique.
From Avner Shaked I learned a lot about game theory and its place in the world.
Rani Spiegler whose work inspired Chapter 2 supported me very much. Philipp
Weinschenk is the coauthor of the paper presented in Chapter 3. I enjoyed very
much to work with him.
I would also like to thank my o ce mates for the discussions we had and for the
good time together: Wei Ding, Ferdinand Gider, Jasmin Gider, Thomas Rieck and
Christian Westheide.
Many discussions and advice from others helped me to improve my work as well.
I especially want to thank Konstanze Albrecht, Marc Armstrong, Olivier Bos,
Gary Charness, Vincent Crawford, Christoph Engel, Emma von Essen, Armin Falk,
Thomas Gall, Alex Gershkov, Susanne Goldluc ke, Paul Heidhues, Martin Hellwig,
Fabian Herweg, Jos Jansen, Philippe Jehiel, Wilbert Kallenberg, Frederik Kaster,
Kai Konrad, Sebastian Kranz, Lutz Mattner, Alexander Morell, Johannes Munster,
Petra Nieken, Juliane Parys, Dan Silverman and Michael Wegener. Of course I also
want to thank the many others that supported me and gave helpful comments on
my projects.
The Bonn Graduate School of Economics is a great place to learn and to develop
and discuss ideas. I would like to thank Urs Schweizer for his enduring e ort in the
school and all the others behind. I also want to thank Uwe Sunde for encouraging
me to take up graduate studies, as well as Armin Falk, Ingo Lieb, Benny Moldovanu,
Frank Riedel and Klaus Sandmann for their advice and encouragement.
I am deeply indebted to my family and to my friends. This thesis is dedicated to
them, especially to my parents.Contents
Introduction 1
1 Asymmetric All-Pay Auctions with Two Types 9
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 The Two Bidder Case . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 All-Pay Auctions with Random Participation . . . . . . . . . . . . . . 20
1.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.1 Disclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.2 Endogenous Choice of Type-Probabilities . . . . . . . . . . . . 31
1.5.3 Competing Contests . . . . . . . . . . . . . . . . . . . . . . . 33
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2 Welfare in Markets where Consumers Rely on Word of Mouth 45
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3 Characterization of All Equilibria . . . . . . . . . . . . . . . . . . . . 53
2.4 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
i3 Rebates in a Bertrand Game 67
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 Characterization of Equilibria . . . . . . . . . . . . . . . . . . . . . . 71
3.3.1 Atomless Pricing for Moderate Rebates . . . . . . . . . . . . . 71
3.3.2 From Bertrand to Monopoly . . . . . . . . . . . . . . . . . . . 75
3.4 The Generalized Model . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4.1 Homogeneous Customers . . . . . . . . . . . . . . . . . . . . . 79
3.4.2 Heterogeneous Customers . . . . . . . . . . . . . . . . . . . . 79
3.5 Welfare and Customers’ Coordination Problem . . . . . . . . . . . . . 81
3.6 Endogenous Rebates . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.7 Concluding Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4 Second-Price Auctions with Information Release 85
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2 Advertising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.1 Optimality of Concentrated Advertising . . . . . . . . . . . . 93
4.2.2 Comparisons to Welfare Maximization . . . . . . . . . . . . . 95
4.2.3 Dispersion of Valuations . . . . . . . . . . . . . . . . . . . . . 97
4.2.4 Reserve Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.3 Information Release . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.3.1 Concentration of Information . . . . . . . . . . . . . . . . . . 100
4.3.2 Preliminary Information . . . . . . . . . . . . . . . . . . . . . 101
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
ii4.4.1 Selling Information . . . . . . . . . . . . . . . . . . . . . . . . 102
4.4.2 More General Cost Functions . . . . . . . . . . . . . . . . . . 102
4.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Optimal Disclosure of Costly Information Packages in Auctions 107
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.3 Indivisible Information . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4 Divisible with Two Bidders . . . . . . . . . . . . . . . . . 115
5.5 Divisible Information with More than Two Bidders . . . . . . . . . . 123
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Bibliography 125
Appendices 139
A Proofs of Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
B Proofs of Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
C Proofs of Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
D Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 164
D.1 Concavity Results for First and Second Order Statistics . . . . 164
D.2 The Decision Problem . . . . . . . . . . . . . . . . . . . . . . 170
D.3 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
E Proofs of Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
iiiivList of Figures
1.1 Strategy Supports under (A1) and (A2) . . . . . . . . . . . . . . . . . 17
1.2 Strategy Supports under (A1), not (A2), and (A3) . . . . . . . . . . . 17
1.3 Strategy Supports under (A1), not (A2), and not (A3) . . . . . . . . 18
1.4 Supports of the Bidders’ Strategies for n = 5 . . . . . . . . . . . . . . 22
1.5 Aggregate E ort when V =V and V = 1 V . . . . . . . . . . . . 38A B
1.6 Aggregate E ort when V = 1 and V =V . . . . . . . . . . . . . . . 39A B
1.7 Limit Proportion of Group 1 Bidders Choosing the Local Contest . . 42
1.8 Limit Distribution of Bidders across Contests . . . . . . . . . . . . . 43
2.1 Expected Social Welfare . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2 Expected Healers’ Aggregate Surplus . . . . . . . . . . . . . . . . . . 60
2.3 Expected Patients’ Aggregate Surplus . . . . . . . . . . . . . . . . . . 61
3.1 Boundaries of the Strategy Supports . . . . . . . . . . . . . . . . . . 72
3.2 Strategy Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3 Pricing Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4 Market Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.1 Payo s from Di erent Allocations in Example 5.2 . . . . . . . . . . . 118
5.2 Maximal Loss in Example 5.2 . . . . . . . . . . . . . . . . . . . . . . 119
5.3 Payo s from Di erent Allocations in Example 5.4 . . . . . . . . . . . 123
vD.1 Constructing a Concave Dominating Sequence . . . . . . . . . . . . . 187
vi