Draft Auctions

We introduce draft auctions, which is a sequential auction format where at each iteration players bid for the right to buy items at a fixed price. We show that draft auctions offer an exponential improvement in social welfare at equilibrium over sequential item auctions where predetermined items are auctioned at each time step. Specifically, we show that for any subadditive valuation the social welfare at equilibrium is an $O(\log^2(m))$-approximation to the optimal social welfare, where $m$ is the number of items. We also provide tighter approximation results for several subclasses. Our welfare guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes, via the smooth-mechanism framework. Of independent interest, our techniques show that in a combinatorial auction setting, efficiency guarantees of a mechanism via smoothness for a very restricted class of cardinality valuations, extend with a small degradation, to subadditive valuations, the largest complement-free class of valuations. Variants of draft auctions have been used in practice and have been experimentally shown to outperform other auctions. Our results provide a theoretical justification

On the stability of generalized second price auctions with budgets

The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.Peer ReviewedPostprint (author's final draft

Auctions: Theory and Practice

This book is a non-technical introduction to auction theory; its practical application in auction design (including many examples); and its uses in other parts of economics. It can be used for a graduate course on auction theory, or – by picking selectively – an advanced undergraduate or MBA course on auctions and auction design. Part A introduces the basic theory. Part B shows how modern auction-theoretic tools illuminate a range of mainstream economic questions that are superficially unconnected with auctions. Part C discusses practical auction design. Part D describes the one-hundred-billion dollar 3G mobile-phone license auctions. None of the writing is technical, except in the Appendices. The material was presented as the inaugural (2003) Toulouse Lectures in Economics and is forthcoming at Princeton University Press. This document contains the Contents, Preface and Introduction to the book. A draft of the FULL BOOK is available at http://www.paulklemperer.org.Auctions, Bidding, Auction Theory, Mechanism Design, Telecommunications, Spectrum Auctions, 3G, UMTS

Outside options: another reason to choose the first-price auction

Pre-print draft dated October 2005. Final version published by Elsevier; available online at http://www.sciencedirect.com/In this paper we study equilibrium and experimental bidding behaviour in first-price and second-price auctions with outside options. We find that bidders do respond to outside options and to variations of common knowledge about competitors’ outside options. However, overbidding in first-price auctions is significantly higher with outside options than without. First-price auctions yield more revenue than second-price auctions. This revenue-premium is significantly higher with outside options. In second-price auctions the introduction of outside options has only a small effect

Asymmetric first-price auctions with uniform distributions: Analytic solutions to the general case

Draft version dated December 25, 2007 originally deposited in SSRN working paper series. Final version published by Springer; available online at http://www.springer.com/While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions

An experimental investigation of entry cost effects in sealed bid dollar auctions

Discussion paperIn numerous auction settings potential bidders incur costs to enter the auction. Such costs may potentially influence bidder’s behavior subsequently. In this paper we experimentally study the effect of entry costs on bidding and entry behavior, through a complete information common value auction. We run first and second price auctions both with and without entry costs. We find that with entry costs, players on average bid lower in first price auctions, while in second price auctions the average bids are higher, compared to bids in the corresponding no entry fee auctions.Author's draft issued as discussion paper. Final version published by Elsevier; available online at http://www.sciencedirect.com

Efficient multi-attribute auctions considering supply disruption

Although supply disruption is ubiquitous because of natural or man-made disasters, many firms still use the price-only reverse auction (only the cost is considered) to make purchase decisions. We first study the suppliers’ equilibrium bidding strategies and the buyer’s expected revenue under the first- and second-price price-only reverse auctions when the suppliers are unreliable and have private information on their costs and disruption probabilities. We show that the two auctions are equivalent and not efficient. Then we propose two easily implementable reverse auctions, namely the first-price and second-price format announced penalty reverse auction (APRA), and show that the “revenue equivalence principle” holds, i.e., the two auctions generate the same ex ante expected profit to the buyer. We further show that the two reverse auctions are efficient and “truth telling” is the suppliers’ dominant strategy in the second-price format APRA. We conduct numerical studies to assess the impacts of some parameters on the bidding strategies, the buyer’s profit and social profitPeer ReviewedPostprint (author's final draft