Linear Bid in Asymmetric First-Price Auctions

Linear Bid in Asymmetric First-Price Auctions
Author: Tadanobu Tanno
Publisher:
Total Pages: 0
Release: 2009
Genre:
ISBN:

We propose a necessary and sufficient condition for the existence of the eqilibrium linear bid in asymmetric first-price auctions with two bidders and uniform distributions. Introducing asymmetry in linear symmetric equilibrium increases expected revenue subject to constant expected sum of valuations. If auctions are asymmetric, the revenue in the linear equiibrium is larger than that in second-price auctions. If auctions in simple case are similar enough, the revenue in the first-price auction moves close to the optimal revenue as auctions are asymmetric. If auctions are similar enough, the linear equilibrium more efficiently allocates the item than the optimal mechanism.

Sequential Bidding in Asymmetric First Price Auctions

Sequential Bidding in Asymmetric First Price Auctions
Author: Gal Cohensius
Publisher:
Total Pages: 31
Release: 2014
Genre:
ISBN:

We study asymmetric first price auctions in which bidders place their bids sequentially, one after the other and only once. We show that with a strong bidder and a weak bidder (in terms of first order stochastic dominance of their valuations distribution function), when the asymmetry between the bidders is large enough the expected revenue in the sequential bidding first price auction (when the strong bidder bids first) is higher than in the simultaneous bidding first price auction as well as in the second price auction. The expected payoff of the weak bidder is also higher in the sequential first price auction. Therefore a seller interested in increasing revenue facing asymmetric bidders may find it beneficial to order them and let them bid sequentially instead of simultaneously. In terms of efficiency, both the simultaneous first price auction and the sequential first price auction cannot guarantee full efficiency (as opposed to a second price auction which guarantees full efficiency). The sequential bidding auction when the stronger bidder bids first achieves lower efficiency than the simultaneous auction. However, when the order is reversed and bidders are asymmetric enough the sequential first price auction achieves higher efficiency than the simultaneous one.

Asymmetric First-Price Auctions With Uniform Distributions

Asymmetric First-Price Auctions With Uniform Distributions
Author: Todd R. Kaplan
Publisher:
Total Pages: 43
Release: 2007
Genre:
ISBN:

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.

First Price Auctions with General Information Structures

First Price Auctions with General Information Structures
Author: Dirk Bergemann
Publisher:
Total Pages: 0
Release: 2017
Genre: Auctions
ISBN:

We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative bidding mechanisms.

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.

Ranking Sealed High-Bid and Open Asymmetric Auctions

Ranking Sealed High-Bid and Open Asymmetric Auctions
Author: arrison heng
Publisher:
Total Pages: 0
Release: 2005
Genre:
ISBN:

For an important family of asymmetric auctions, we show that the seller's expected revenue is higher in the sealed high-bid auction than in the open auction. This is true for any arbitrary numbers of weak and strong buyers. The family has linear equilibrium bidding strategies, and provides a fertile ground for research in asymmetric auctions. We establish many interesting properties of the linear asymmetric auction model. Revenue comparisons for the two auction formats are performed using data observed in U.S. forest timber auctions. By taking realistic parameters fitting the data, and compare the theoretical predictions of the revenues from the two auction formats, we show that the revenue difference is minimal with a fixed number of participants. When the difference in participation is taken into account, the revenue difference predicted by the linear model is quite similar to the empirical results of Athey, Levin and Seira (2004).

Common Value Auctions with Asymmetric Bidder Information

Common Value Auctions with Asymmetric Bidder Information
Author: Priyodorshi Banerjee
Publisher:
Total Pages: 37
Release: 2008
Genre:
ISBN:

We study common value auctions with two asymmetrically informed bidders using a simple binary model. A unique, generically asymmetric, mixed-strategy equilibrium exists for the first-price auction. Bidders get positive payoffs, with a superiorly informed bidder getting a higher payoff. One of the bidders submits a higher bid than the other on average: aggressive bidding is not necessarily associated with inferiority of information. A continuum of pure-strategy equilibria exist for the second-price auction. If bidders play the unique symmetric equilibrium strategies, second-price auctions are generically revenue-dominant. A change in the degree of asymmetry in general has an ambiguous effect on revenue.

Elicited Bid Functions in (A)Symmetric First-Price Auctions

Elicited Bid Functions in (A)Symmetric First-Price Auctions
Author: Paul Pezanis-Christou
Publisher:
Total Pages: 35
Release: 2005
Genre:
ISBN:

We report on a series of experiments that examine bidding behavior in first-price sealed bid auctions with symmetric and asymmetric bidders. To study the extent of strategic behavior, we use an experimental design that elicits bidders complete bid functions in each round (auction) of the experiment. In the aggregate, behavior is consistent with the basic equilibrium predictions for risk neutral or homogenous risk averse bidders (extent of bid shading, average seller's revenues and deviations from equilibrium). However, when we look at the extent of best reply behavior and the shape of bid functions, we find that individual behavior is not in line with the received equilibrium models, although it exhibits strategic sophistication.