Essays on Multi-unit Auctions: Theory and Experiment Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Jinsoo Bae, M.A. Graduate Program in Economics The Ohio State University 2020 Dissertation Committee John H. Kagel, Advisor Dan Levin Paul J. Healy 1 Copyrighted by Jinsoo Bae 2020 2 Abstract This dissertation contains three essays on the topic of multi-unit auctions. In Chapter 1, I experimentally investigate implications of weak and strong budget constraints on two share auctions, the uniform price and the proportional share auction, compared to the first price auction. Under the strong budget constraint, the two share auctions raise higher revenue than the first price auction, in contrast to studies without budget constraints. More surprisingly, the proportional share auction achieves higher efficiency than the first price auction despite its inherently inefficient allocation rule. The proportional share auction performed better than the uniform price auction under the strong budget constraint, but under the weak budget constraint, the uniform price auction performed the same or better than the proportional share auction. In Chapter 2, We experimentally investigate the Generalized Second Price (GSP) auction used to sell advertising positions in online search engines. Two contrasting click through rates (CTRs) are studied, under both static complete and dynamic incomplete information settings. Subjects consistently bid above the Vikrey–Clarke–Grove’s (VCG) like equilibrium favored in the theoretical literature. However, bidding, at least qualitatively, satisfies the contrasting outcomes predicted under the two CTRs. For both CTRs, outcomes under the static complete information environment are similar to those in later rounds of the dynamic incomplete information environment. This supports the theoretical ii literature that uses the static complete information model as an approximation to the dynamic incomplete information under which advertising positions are allocated in field settings. Chapter 3 studies a pro-competitive effect of joint bidding in multi-unit uniform price auctions where bidders have private values and demand different quantities of units. I analyze a simple model with three identical items for sale, two small bidders each demanding a single unit, and a big bidder demanding two units. I show that joint bidding of the two small bidders, which recovers the symmetry of bidders, enhances competition among the bidders and increases efficiency and revenue of the auction. iii Dedication To my parents iv Acknowledgments The completion of this dissertation would not have been possible without the continual support and encouragement from John Kagel. I thank Dan Levin for his wisdom, insight and advice. I would also like to thank Paul J. Healy for his guidance and his efforts to maintain the HAKK reading group where I received tremendous feedback. I am also grateful to Yaron Azrieli, Lixin Ye, James Peck, Huanxing Yang, Ian Krajbich, John Rehbeck and other faculty members in the Department of Economics for helpful comments. Chapter 2 of this dissertation was written in collaboration with John Kagel. I have benefited immensely from working with him. I received funding from National Science Foundation (SES-1919450), the Journal of Money, Credit, and Banking, and Alumni Grants for Graduate Research and Scholarship for research in Chapter 1. The research in Chapter 2 was supported by National Science Foundation (SES-1630288) and the Journal of Money, Credit, and Banking. I thank John- David Slaughter, Rick Tobin, Tiffany Garner, and other staff members for their help to run experiment sessions. I would like to extend a special thanks to my family and dear friends for your care and encouragement throughout my educational career. I thank my parents, Euiyeol Bae and Ilsoon Shin, for their unending love and support. I also thank my sister, Soyoon Bae for v her continual care and love. I am also grateful to Sangjun Yea, Ben Casner, Renkun Yang and OSub Kwon for being with me during my Ph.D program. Last but not the least, I thank God for enabling me to reach this far. vi Vita 2012 . B.A. Economics, Yonsei University 2014 . M.A. Economics, Yonsei University 2015 . M.A. Economics. The Ohio State University 2015-2018 . Graduate Teaching Associate, Department of Economics, The Ohio State University 2018-2020 . Graduate Research Associate, Department of Economics, The Ohio State University Publications Bae, J. and Kagel, J. H. (2019). An experimental study of the generalized second price auction. International Journal of Industrial Organization, 63, 44-68. Fields of Study Major Field: Economics vii Table of Contents Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iv Acknowledgments............................................................................................................... v Vita .................................................................................................................................... vii List of Tables ..................................................................................................................... xi List of Figures ................................................................................................................... xii Chapter 1. Selling Shares to Budget Constrained Bidders: An Experimental Study of Two Share Auctions .................................................................................................................... 1 1.1. Introduction .............................................................................................................. 1 1.2. Literature review ...................................................................................................... 6 1.3. Theoretical framework ............................................................................................. 9 1.4. Experimental design and hypotheses ..................................................................... 12 1.5. Experimental procedures ....................................................................................... 17 1.6. Experimental results............................................................................................... 20 1.6.1. Efficiency and Revenue .......................................................................................... 21 1.6.2. Bidding behavior ..................................................................................................... 25 1.6.2.1. First price auction .................................................................................... 25 1.6.2.2. Proportional share auction ....................................................................... 28 1.6.2.3. Uniform price auction .............................................................................. 30 1.6.2.4. Uniform price auction – modified rule .................................................... 36 1.6.3. Dominated strategy ................................................................................................. 39 1.6.3.1. Proportional share auction ....................................................................... 39 1.6.3.2. Uniform price auction .............................................................................. 41 1.6.3.3. Uniform price auction – modified rule .................................................... 44 1.7. Summary and conclusion ....................................................................................... 47 viii Chapter 2. An Experimental Study of the Generalized Second Price Auction ................ 50 2.1. Introduction ............................................................................................................ 50 2.2. Theoretical framework .......................................................................................... 55 2.3. Experimental design and procedures ..................................................................... 59 2.4. Predicted Outcomes and Propositions to be Investigated ...................................... 62 2.5. Experimental results............................................................................................... 64 2.5.1. Efficiency and revenue ........................................................................................... 64 2.5.2. Bidding over Time .................................................................................................. 70 2.5.3. Nash Equilibrium Bidding and Best Responding ................................................... 78 2.6. Summary and Conclusions .................................................................................... 84 Chapter 3. A Pro-Competitive Effect of Joint Bidding in Multi-Unit Uniform Price Auction with Asymmetric Bidders ................................................................................... 87 3.1. Introduction ............................................................................................................ 87 3.2. The Model .............................................................................................................. 89 3.2.1. Without Joint Bidding ............................................................................................