Three Essays on Auction Theory

Three Essays on Auction Theory
Author: Xiaoshu Xu
Publisher:
Total Pages: 63
Release: 2011
Genre:
ISBN:

Abstract: My dissertation consists of three chapters in theoretical auction analysis. The first chapter considers optimal sequential auctions with new bidders arriving in each period. The second chapter examines how resale affects bidding strategies and auction outcomes in an auction environment with costly entry. The third chapter investigates how resale affects bidding strategies and auction outcomes in a sequential auction setting where the values of items auctioned in different periods exhibit synergies. The first chapter gives a full characterization of the optimal sequential second-price (or ascending English) auctions with sequentially arriving bidders. There are n bidders in the first period and m new bidders arrive in the second period. Based on the auctioneer's commitment power, we study two cases: full commitment and noncommitment. In both cases, we establish the existence of a symmetric equilibrium characterized by a threshold strategy - -a bidder does not bid in the first auction when her valuation is below this threshold and bids according to an increasing function otherwise. In the noncommitment case, the auctioneer chooses an optimal reserve price to maximize the expected revenue from the second period; thus her decision of whether to include previous bidders as potential buyers is endogenously determined by the reserve price in the first auction. This might create multiple equilibria depending on the beliefs of the auctioneer and the bidders. We apply a fairly intuitive rule to establish the uniqueness. We also extend our analysis to allow for opportunities for resale, where the winner in the first auction can opt to resell the item to new bidders. The second chapter, joint with Dan Levin and Lixin Ye, studies how resale affects auctions with costly entry in a model where an arbitrary number of bidders possess two-dimensional private information signals: entry costs and valuations. We establish the existence of symmetric entry equilibrium and identify sufficient conditions under which the equilibrium is unique. Our analysis suggests that the opportunity of resale induces motivation for both speculative entry and bargain hunting abstentions. By following the uniform distribution for numerical analysis, our results suggest that while the entry probability and efficiency are always higher when resale is allowed, the auctioneer's expected revenue is lower when resale is allowed for almost all parameter values. We also compare this model to one where bidders may follow "strong" or "weak" distributions in terms of valuations. The third chapter, joint with Dan Levin and Lixin Ye, studies a sequential second-price auction of two objects with two bidders, where the winner of the package obtains a synergy from the second object. If reselling after the two auctions occurs, it proceeds as either monopoly or monopsony take-it-or-leave-it offer. I find that a post-auction resale has a significant impact on bidding strategies in the auctions. When seller makes a take-it-or-leave-it offer in resale, there is no equilibrium where at least one bidder reveals her type with positive probability. When buyer makes the offer instead, there exist symmetric increasing equilibrium strategies for both items. While allowing resale always improves efficiency, I demonstrate that the effect of resale is ambiguous on expected revenue as Ill as the probability of exposure. I also extend this model to allow for three bidders and provide the equilibrium analysis.

Asymmetric Auctions with Resale

Asymmetric Auctions with Resale
Author: Isa Emin Hafalir
Publisher:
Total Pages: 39
Release: 2006
Genre:
ISBN:

We study equilibria of first- and second-price auctions with resale in a model with independent private values. With asymmetric bidders, the resulting inefficiencies create a motive for post-auction trade. In our basic model, resale takes place via monopoly pricing - the winner of the auction makes a take-it-or-leave-it offer to the loser after updating his prior beliefs based on his winning. We show that a first-price auction with resale has a unique monotonic equilibrium. Our main result is that with resale, the expected revenue from a first-price auction exceeds that from a second-price auction. The results extend to other resale mechanisms: monopsony and, more generally, probabilistic k-double auctions. The inclusion of resale possibilities thus permits a general revenue ranking of the two auctions that is not available when these are excluded.

Auction Theory

Auction Theory
Author: Vijay Krishna
Publisher: Academic Press
Total Pages: 319
Release: 2002-03-13
Genre: Business & Economics
ISBN: 012426297X

"Vijay Krishna's book provides a very thorough and patient presentation of auction theory, starting from the most basic analysis and graduating to sophisticated, state of the art theory, including multi-unit auctions. This book covers a very wide range of auction topics, providing a clear and accessible treatment. The theory is presented in a careful and easily understood style accessible to honors undergraduates as well as all economics graduate students. Krishna's book will certainly become the central book on auction theory." --R. Preston McAfee, Murray S. Johnson Chair in Economics, University of Texas "This book not only sets out much of the theoretical literature on auctions-including results that are very recent-but does so with a clarity, elegance, and rigor that is characteristic of Vijay Krishna's work." --Eric Maskin, A.O. Hirschman Professor of Social Science, Institute for Advanced Study, Princeton, New Jersey "The book gives a superb presentation of auction theory, with clear and concise proofs of all results. It is essential reading for any serious student of auctions." --Peter Cramton, Professor of Economics, University of Maryland "This is the book we have been waiting for: a high level treatment of auction theory that carefully presents the technical details necessary for an in depth understanding of the main themes of auction theory, ideal as a basis for a graduate course, and by an author who has himself made important contributions to the subject." --Paul Klemperer, Edgeworth Professor of Economics, Nuffield College, University of Oxford, United Kingdom Through accessible, detailed examinations of themes central to auction theory, Vijay Krishna explores auctions and competitive bidding as games of incomplete information. His results on bidding strategies, efficiency, and revenue maximization and his clear proofs for each proposition make this book both the standard reference on auctions and the first source of authoritative information about multiunit auctions. Well organized and featuring straightforward intuition, Auction Theory's depth and breadth lay bare the complexity and utility of this growing field.

Multi-Object Auctions with Resale

Multi-Object Auctions with Resale
Author: Marco Pagnozzi
Publisher:
Total Pages: 0
Release: 2013
Genre:
ISBN:

We analyze the effects of resale through bargaining in multi-object uniform-price auctions with asymmetric bidders. The possibility of resale affects bidders' strategies, and hence the allocation of the objects on sale and the seller's revenue. Our experimental design consists of four treatments: one without resale and three resale treatments that vary both the bargaining mechanism and the amount of information available in the resale market. As predicted by theory: without resale, asymmetry among bidders reduces demand reduction; resale increases demand reduction by high-value bidders; low-value bidders speculate by bidding more aggressively with resale. Therefore, resale induces speculation and demand reduction which reduce auction efficiency. In contrast to what is usually argued, resale does not necessarily increase final efficiency and may not reduce the seller's revenue. Features of the resale market that tend to increase its efficiency also reduce the seller's revenue.