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Optimal Design of Dutch Auctions with Discrete Bid Levels. Doctor Of

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Optimal Design of Dutch Auctions with Discrete Bid Levels. Doctor Of OPTIMAL DESIGN OF DUTCH AUCTIONS WITH DISCRETE BID LEVELS Zhen Li, B.A., M.S. Dissertation Prepared for the Degree of DOCTOR OF PHILOSOPHY UNIVERSITY OF NORTH TEXAS May 2010 APPROVED: Ching-Chung Kuo, Major Professor and Program Coordinator for Operations Management Robert J. Pavur, Minor Professor Grant Miles, Committee Member Vicki L. Goodwin, Chair of the Department of Management O. Finley Graves, Dean of the College of Business Michael Monticino, Dean of the Robert B. Toulouse School of Graduate Studies Li, Zhen. Optimal design of Dutch auctions with discrete bid levels. Doctor of Philosophy (Management), May 2010, 224 pp., 34 tables, 30 illustrations, references, 142 titles. The theory of auction has become an active research area spanning multiple disciplines such as economics, finance, marketing and management science. But a close examination of it reveals that most of the existing studies deal with ascending (i.e., English) auctions in which it is assumed that the bid increments are continuous. There is a clear lack of research on optimal descending (i.e., Dutch) auction design with discrete bid levels. This dissertation aims to fill this void by considering single-unit, open-bid, first price Dutch auctions in which the bid levels are restricted to a finite set of values, the number of bidders may be certain or uncertain, and a secret reserve price may be present or absent. These types of auctions are most attractive for selling products that are perishable (e.g., flowers) or whose value decreases with time (e.g., air flight seats and concert tickets) (Carare and Rothkopf, 2005). I began by conducting a comprehensive survey of the current literature to identify the key dimensions of an auction model. I then zeroed in on the particular combination of parameters that characterize the Dutch auctions of interest. As a significant departure from the traditional methods employed by applied economists and game theorists, a novel approach is taken by formulating the auctioning problem as a constrained mathematical program and applying standard nonlinear optimization techniques to solve it. In each of the basic Dutch auction model and its two extensions, interesting properties possessed by the optimal bid levels and the auctioneer’s maximum expected revenue are uncovered. Numerical examples are provided to illustrate the major propositions where appropriate. The superiority of the optimal strategy recommended in this study over two commonly-used heuristic procedures for setting bid levels is also demonstrated both theoretically and empirically. Finally, economic as well as managerial implications of the findings reported in this dissertation research are discussed. Copyright 2010 by Zhen Li ii TABLE OF CONTENTS Page LIST OF TABLES ........................................................................................................................ vii LIST OF ILLUSTRATIONS ......................................................................................................... ix CHAPTER 1 INTRODUCTION ................................................................................................... 1 1.1 Auction, Auctioneer and Auction House .............................................................................. 1 1.2 Historical Background .......................................................................................................... 2 1.3 Importance of Auction .......................................................................................................... 3 1.4 Taxonomy of Auctions ......................................................................................................... 5 1.5 Dutch Auction ....................................................................................................................... 8 1.6 Key Concepts in Auction Theory ......................................................................................... 9 1.7 Purpose of Study ................................................................................................................. 12 CHAPTER2 LITERATURE REVIEW ....................................................................................... 14 2.1 Overview ............................................................................................................................. 14 2.2 Price Determination ............................................................................................................ 15 2.3 Direction of Price Change ................................................................................................... 17 2.4 Transparency of Information .............................................................................................. 18 2.5 Lot Size ............................................................................................................................... 22 2.6 Number of Bidders .............................................................................................................. 24 2.7 Reserve Price ...................................................................................................................... 26 2.8 Bid Increment/Decrement ................................................................................................... 29 2.9 Focus and Uniqueness of Study .......................................................................................... 32 CHAPTER 3 A BASIC DUTCH AUCTION MODEL WITH DISCRETE BID LEVELS ....... 40 3.1 Introduction ......................................................................................................................... 40 3.2 Auction Model .................................................................................................................... 40 3.3 Existence of Global Optimality .......................................................................................... 43 3.4 Properties of Optimal Bid Levels ....................................................................................... 45 3.5 Properties of Maximum Expected Revenue ....................................................................... 48 3.6 A Comparative Study .......................................................................................................... 50 3.6.1 Strategy E ..................................................................................................................... 51 iii 3.6.2 Strategy D .................................................................................................................... 52 3.6.3 Revenue Comparison ................................................................................................... 54 3.7 Numerical Illustrations........................................................................................................ 56 3.8 Simulation Analysis ............................................................................................................ 67 3.9 Conclusions ......................................................................................................................... 69 CHAPTER 4 A DUTCH AUCTION MODEL WITH AN UNCERTAIN NUMBER OF BIDDERS ..................................................................................................................................... 70 4.1 Introduction ......................................................................................................................... 70 4.2 A New Model ...................................................................................................................... 71 4.3 Existence and Properties of Optimal Bid Levels ................................................................ 73 4.4 Properties of Maximum Expected Revenue ....................................................................... 76 4.5 A Comparative Study .......................................................................................................... 78 4.6 Numerical Illustrations........................................................................................................ 81 4.7 Simulation Analysis ............................................................................................................ 93 4.8 Conclusions ......................................................................................................................... 95 CHAPTER 5 A DUTCH AUCTION MODEL WITH A SECRET RESERVE PRICE AND AN UNCERTAIN NUMBER OF BIDDERS ..................................................................................... 97 5.1 Introduction ......................................................................................................................... 97 5.2 Another New Model ........................................................................................................... 99 5.3 Existence and Properties of Optimal Bid Levels .............................................................. 100 5.4 Properties of Maximum Expected Revenue ..................................................................... 106 5.5 A Comparative Study ........................................................................................................ 109 5.5.1 Strategy E ................................................................................................................... 109 5.5.2 Strategy D .................................................................................................................. 111 5.5.3 Revenue Comparison ................................................................................................
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