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

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

Asymmetric First-Price Auctions With Uniform Distributions

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

Sequential Bidding in Asymmetric First Price Auctions

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

Linear Bid in Asymmetric First-Price Auctions

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

First-Price Auctions When the Ranking of Valuations is Common Knowledge

First-Price Auctions When the Ranking of Valuations is Common Knowledge
Author: Michael Landsberger
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Total Pages: 0
Release: 2017
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We consider an augmented version of the symmetric private value auction model with independent types. The augmentation, intended to illustrate reality, concerns information bidders have about their opponents. To the standard assumption that every bidder knows his type and the distribution of types is common knowledge we add the assumption that the ranking of bidders' valuations is common knowledge. This set-up induces a particular asymmetric auction model that raises serious technical difficulties. We prove existence and uniqueness of equilibrium in pure strategies in the two bidder case. We also show that the model generally has no analytic solution. If the distribution of valuations is uniform, both bidders bid pointwise more aggressively relative to the standard symmetric case. However, this property does not apply to all distributions of valuations. Finally, we also provide a numerical solution of equilibrium bid functions for the uniform distribution case.