Two Stage Auctions

This book provides a comprehensive introduction to modern auction theory and its important new applications. It is written by a leading economic theorist whose suggestions guided the creation of the new spectrum auction designs. Aimed at graduate students and professionals in economics, the book gives the most up-to-date treatments of both traditional theories of 'optimal auctions' and newer theories of multi-unit auctions and package auctions, and shows by example how these theories are used. The analysis explores the limitations of prominent older designs, such as the Vickrey auction design, and evaluates the practical responses to those limitations. It explores the tension between the traditional theory of auctions with a fixed set of bidders, in which the seller seeks to squeeze as much revenue as possible from the fixed set, and the theory of auctions with endogenous entry, in which bidder profits must be respected to encourage participation.

The present paper studies a simple two-stage model of an all-pay auction under complete information. All-pay auctions are often used to model competition with irreversible investments such as political lobbying, and in the existing models, the equilibrium outcomes are quite different from the winner-pay auctions (under complete information): The unique equilibrium is in non-degenerate mixed strategies in the sealed-bid all-pay auction, and the highest value bidder wins at (virtually) no cost in the dollar auction. In sharp contrast with those existing models, the equilibrium outcome in the present setting is almost identical to the winner-pay auctions. That is, (a) the highest value bidder wins with probability one, and (b) the revenue of the seller is equal to the second highest value among the bidders. Also, from a mechanism-design point of view, the present game form is more robust than other all-pay mechanisms in that the seller does not need any information about the bidders' valuations. Although the analysis focuses on the two-bidder two-stage case, the results extend to arbitrary numbers of bidders and stages.

A synthesis of theoretical and practical research on combinatorial auctions from the perspectives of economics, operations research, and computer science.

Are all film stars linked to Kevin Bacon? Why do the stock markets rise and fall sharply on the strength of a vague rumour? How does gossip spread so quickly? Are we all related through six degrees of separation? There is a growing awareness of the complex networks that pervade modern society. We see them in the rapid growth of the internet, the ease of global communication, the swift spread of news and information, and in the way epidemics and financial crises develop with startling speed and intensity. This introductory book on the new science of networks takes an interdisciplinary approach, using economics, sociology, computing, information science and applied mathematics to address fundamental questions about the links that connect us, and the ways that our decisions can have consequences for others.

A guide to modeling and analyzing auctions, with the applications of game theory and auction theory to real-world auction decision making. Auctions are highly structured market transactions primarily used in thin markets (markets with few participants and infrequent transactions). In auctions, unlike most other markets, offers and counteroffers are typically made within a structure defined by a set of rigid and comprehensive rules. Because auctions are essentially complex negotiations that occur within a fully defined and rigid set of rules, they can be analyzed by game theoretic models more accurately and completely than can most other types of market transactions. This book offers a guide for modeling, analyzing, and predicting the outcomes of auctions, focusing on the application of game theory and auction theory to real-world auction design and decision making. After a brief introduction to fundamental concepts from game theory, the book explains some of the more significant results from the auction theory literature, including the revenue (or payoff) equivalence theorem, the winner's curse, and optimal auction design. Chapters on auction practice follow, addressing collusion, competition, information disclosure, and other basic principles of auction management, with some discussion of auction experiments and simulations. Finally, the book covers auction experience, with most of the discussion centered on energy and telecommunications auctions, which have become the proving ground for many new auction designs. A clear and concise introduction to auctions, auction design, and auction strategy, this Primer will be an essential resource for students, researchers, and practitioners.

This paper studies second-price auctions with a temporary Buy-It-Now price (BIN auctions) using a two-stage model, in which two groups of bidders enter the auction at different times. The early bidders are offered a Buy-It-Now (BIN) option to purchase the item immediately at a listed price (BIN price). If no early bidder accepts the BIN option, an additional group of bidders (late bidders) enter the auction and both groups of bidders participate in a second-price sealed-bid auction without BIN option. When bidders are risk averse with concave utility functions, we establish the existence and uniqueness of a cutoff equilibrium such that an early bidder will accept the BIN option if his valuation is higher than the cutoff valuation. Moreover, bidders are more likely to accept the BIN option when fewer bidders are offered the BIN option. We show that when facing risk averse bidders, the seller can obtain higher expected revenue in BIN auctions than in standard second-price auctions. Furthermore, the expected seller revenue decreases with the number of early bidders. Consequently, the expected seller revenue is higher in the auctions with BIN only available to a subset of bidders than in the auctions with BIN available to all bidders. These results may help explain the popularity of temporary BIN auctions on eBay and the observed high acceptance frequencies of BIN prices in experimental and field studies.

Some of the finest and most recent research in economic and political design is presented. Among the authors are several prominent academics as well as many new and promising researchers. They investigate social choice and electoral systems, auctions, matching, bargaining, coalitional stability and efficiency, regulation, the design of rights, mechanisms, games, hierarchies and information. The book is bound to become a standard reference as a collection displaying where we are and where we are going in a broad spectrum of areas in economic design.