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Buyout Prices in Online Auctions by Shobhit Gupta B Buyout Prices in Online Auctions by Shobhit Gupta B. Tech., Mechanical Engineering (2002) Indian Institute of Technology, Bombay Submitted to the Sloan School of Management in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Operations Research at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2006 ( Massachusetts Institute of Technology 2006. All rights reserved. Author................ ''..Sloan ' School of Management cam May 18, 2006 Certifiedby....... _. 7.."~r~emie Gallien J. Spencer Standish Career Development Professor Thesis Supervisor Acceptedby ..................... .................... James B. Orlin Edward Pennell Brooks Professor of Operations Research, Co-director, Operations Research Center MASSACHUSET'TS INSTITUE OF TECHNOLOGY J L 2 4 2006 LIBRARIES ARCHNVE Buyout Prices in Online Auctions by Shobhit Gupta Submitted to the Sloan School of Management on May 18, 2006, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Operations Research Abstract Buyout options allow bidders to instantly purchase at a specified price an item listed for sale through an online auction. A temporary buyout option disappears once a regular bid above the reserve price is made, while a permanent option remains available until it is exercised or the auction ends. Buyout options are widely used in online auctions and have significant economic importance: nearly half of the auctions today are listed with a buyout price and the option is exercised in nearly one fourth of them. We formulate a game-theoretic model featuring time-sensitive bidders with in- dependent private valuations and Poisson arrivals but endogenous bidding times in order to answer the following questions: How should buyout prices be set in order to maximize the seller's discounted revenue? What are the relative benefits of using each type of buyout option? While all existing buyout options we are aware of currently rely on a static buyout price (i.e. with a constant value), what is the potential ben- efit associated with using instead a dynamic buyout price that varies as the auction progresses? For all buyout option types we exhibit a Nash equilibrium in bidder strategies, argue that this equilibrium constitutes a plausible outcome prediction, and study the problem of maximizing the corresponding seller revenue. In particular, the equilib- rium strategy in all cases is such that a bidder exercises the buyout option provided it is still available and his valuation is above a time-dependent threshold. Our numerical experiments suggest that a seller may significantly increase his utility by introducing a buyout option when any of the participants are time-sensitive. Furthermore, while permanent buyout options yield higher predicted revenue than temporary options, they also provide additional incentives for late bidding and may therefore not be al- ways more desirable. The numerical results also imply that the increase in seller's utility (over a fixed buyout price auction) enabled by a dynamic buyout price is small and does not seem to justify the corresponding increase in complexity. Thesis Supervisor: Jr6mie Gallien Title: J. Spencer Standish Career Development Professor 3 4 Acknowledgments I am deeply indebted to my thesis advisor, Professor Jr6mie Gallien, for his unwa- vering guidance, support and encouragement. His enthusiasm for research, attention to rigor and detail, and limitless knowledge has been a constant source of inspiration guiding me over the last four years. He has been very generous with his time and very supportive of my efforts. Thank you, Jremie! I would also like to thank my thesis committee members, Professor Stephen Graves and Professor Georgia Perakis, for their critical comments and suggestions that have greatly improved the quality of this dissertation. During my years at MIT, I have gained valuable teaching experience for which I am thankful to Professor J6r6mie Gallien, Professor Stephen Graves, Professor John Wyatt and Professor Roy Welsch who very kindly offered me tutoring positions. A very special note of thanks to Professor John Wyatt who gave me his car - owning a car has been a great convenience and luxury and has vastly improved my student life experience. I spent a lot of time in my office at the ORC and am very thankful to my col- leagues for being such a fun group of people and an excellent source of help. I would specially like to thank Pranava Goundan and Raghavendran Sivaraman for their help with all my research problems, and Kwong Meng Teo, Dan Stratila and Alexandre Belloni for being great office-mates. Special thanks to Paulette Mosley, Laura Rose, Andrew Carvalho and Veronica Mignott for their superb administrative assistance and friendship. Finally, I will like to thank Smeet for her love, friendship and care. Of course, this thesis would not have been possible without the unconditional love and support of my parents and sisters who have always believed in me and encouraged me. This dissertation is dedicated to my parents to whom I am eternally grateful for all the values they have instilled in me. 5 6 Contents 1 Introduction 13 1.1 Literature Survey ............ ............. 16 1.1.1 Literature on Online Auctions .................. 16 1.1.2 Literature on Buyout Price auctions . ..... 19 2 Market Environment and Auction Mechanism 25 2.1 Market Environment ........................... 25 2.2 Auction Mechanism ............................ 26 2.3 Model Discussion ............................. 28 3 Static Buyout Prices 33 3.1 Temporary Buyout Option ........................ 33 3.1.1 Outcome Prediction ....................... 34 3.1.2 Equilibrium Refinements ................... .. 45 3.1.3 Seller's Optimization Problem .................. 54 3.2 Permanent Buyout Option ........................ 62 3.2.1 Outcome Prediction ....................... 62 3.2.2 Equilibrium Refinements . 74 3.2.3 Seller's Optimization Problem .. .. 76 4 Dynamic Buyout Prices 79 4.1 Temporary Buyout Option ....................... 79 4.1.1 Outcome Prediction. .. 79 7 4.1.2 Seller's Optimization Problem. 89 4.2 Permanent Buyout Option ............. 93 . .. 4.2.1 Outcome Prediction. 93 4.2.2 Seller's Optimization Problem ..... 98 5 Empirical Analysis, Numerical Results and Comparative DiscussionlO5 5.1 Static buyout prices ................... ......... 105 5.1.1 Equilibrium threshold valuation functions .......... 106 5.1.2 Approximate temporary buyout price .............. 107 5.1.3 Temporary and permanent optimal buyout prices ....... 108 5.1.4 Gain in seller's utility enabled by a buyout price ........ 111 5.2 Dynamic buyout prices . ........ ....... 114 5.3 Empirical Analysis of Bidding Data . ........... 117 5.3.1 eBay Data ............................. 120 5.3.2 YahooData ........... ............ 123 6 Conclusion 129 A Appendix 133 A.1 Proof of Proposition 1 ........... .............. 133 A.2 Expression for Et[max(v, v(2T)+l )1 .............. 134 A.3 Proof of Lemma 8 .............. .............. 135 A.4 Proof of Lemma 10 ............. .............. 141 A.5 Proof of Proposition 2 ..... .............. 143 8 List of Figures 2-1 Snapshot of an online auction webpage ................. 28 5-1 Equilibrium threshold valuation in temporary and permanent buyout price auction . ............ ...... 106 5-2 Optimal temporary buyout price ( = 0.03) .............. 109 5-3 Optimal temporary buyout price ( = 0.03) .............. 110 5-4 Optimal temporary and permanent buyout prices with impatient bid- ders .......... ......... ...... 111 5-5 Relative increase in seller's utility from a temporary buyout option ( = 0.03) ................................. 112 5-6 Relative increase in seller's utility from a permanent buyout option (p = 0.03) ................................. 113 5-7 Relative increase in seller's utility from a temporary buyout option (a = 0.03) ................................. 114 5-8 Relative increase in seller's utility from a permanent buyout option (a = 0.03) ................................. 115 5-9 First activity time as a function of winning bid ............. 121 5-10 Plot of mean first activity time with mean winning bid in a temporary buyout price auction ........................... 124 5-11 Average bid time as a function of winning bid ............. 125 A-1 Threshold valuation vprm......................... 144 9 10 List of Tables 3.1 Optimal buyout price in asymptotic regimes .............. 59 5.1 Percent utility increase achieved by temporary optimal and approxi- mate buyout price .. ..... ..... 108 5.2 Utility increase achieved by fixed and dynamic temporary buyout prices116 5.3 Utility increase achieved by fixed and dynamic permanent buyout prices16 5.4 Summary of auction data with wb < $30, bp > 1.25, and b > 0.8 . 121 5.5 Mean first activity time for different winning bid cutoffs ........ 123 5.6 Summary of auction data with wb > $100, SpbP -> 1.25,· and bpb > 0.8. 125 11 12 Chapter 1 Introduction As they were initially conceived during the last decade of the previous century, online auctions were arguably suffering from two perceived drawbacks relative to posted price mechanisms: waiting time and price uncertainty. In order to render these auctions more attractive to time-sensitive or risk averse participants, many auction sites have since introduced a new feature known as a buyout option, which offers potential buyers the opportunity to instantaneously purchase at a specified price an item put for sale through an online auction. Indeed Mathews (2003b) notes that "one
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