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Unformatted text preview: Auction Theory With Experiments by Rodney J. Garratt 1 April 7, 2011 1 Department of Economics, University of California at Santa Barbara, gar- [email protected] 2 Overview The goal of this text, its supplement, and software is to provide a means of teaching auction theory to advanced undergraduates. The starting premise of this text is that auction theory is intrinsically interesting and practical, but mathematically difficult. As a result it is necessary to (1) find the simplest presentation of the material that still conveys the full power of the results and (2) suitably motivate students to work hard and comprehend the material. We achieve the first task by presenting most of the theoretical results in terms of a special case: symmetric, uniformly distributed use-values with common sup- port. This case allows simple, closed form solutions of bid functions and easy computation of auction revenues. Moreover, this case allows us to demonstrate central results, such as revenue equivalence of standard auction formats, with relative ease. We achieve the second task by using experiments in a completely integrated way. Each topic covered in this text relates to an experiment. Stan- dard theoretical results covered in the text are presented as predictions for behavior in these experiments. The supplement outlines data analysis to test the theory for each experiment and provides discussion points. Sometimes the discussion involves analysis provided by the students in homework exercises that accompany some of the chapters. A list of the experiments used in this text is provided in the Appendix. Target Audience The book is aimed at advanced undergraduates. It requires some knowledge of calculus, real analysis and probability theory. A review of the needed con- cepts is provided in Chapter 2, which is based on a section called Probability Preliminaries, in the unpublished working paper ”A Technical Primer on Auc- tion Theory I: Independent Private Values” by Steven Matthews. Most of the theory presented in the text is game theoretic. As such, our ideal target audi- ence would be students who have already completed an undergraduate course in game theory. However, we understand that this will not always be possi- ble. All we really require is that students understand the notion of a dominant strategy and have a working knowledge of Nash equilibrium. Most intermedi- ate microeconomics courses include one or two chapters on game theory that cover these topics. We regard this to be sufficient. The course includes empir- ical analysis of experimental data; however we do not require students to have taken econometrics. Contents 1 Introduction 5 2 Getting Started 9 2.1 Order Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Conditional Expectations . . . . . . . . . . . . . . . . . . . . . . 13 3 Bidding Behavior 15 3.1 Second-Price Auctions . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.1 Reserve Prices and Entry Fees . . . . . . . . . . . . . . .Reserve Prices and Entry Fees ....
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