Asymmetric First-Price Auctions With Uniform Distributions PDF Download
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Author: Todd R. Kaplan
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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Book Description
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.
Author: Todd R. Kaplan
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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Book Description
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.
Author: Tadanobu Tanno
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Patrick L. Bajari
Publisher:
ISBN:
Category :
Languages : en
Pages : 272
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Book Description
Author: Gal Cohensius
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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Book Description
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.
Author: Michael Landsberger
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Robert Marquez
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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Book Description
We study endogenous participation in asymmetric second price auctions where one bidder is "special". We show seller revenue decreases whenever the special bidder becomes more dominant in the sense of FOSD, or more generally whenever the other bidders' profits are reduced. We also establish an equivalence result for second price auctions - any arbitrary distribution of the special bidder's value is "competitively equivalent" to one that is a power function of the value distribution of the other bidders. Finally, we analyze first-price auctions numerically and show that our results extend to this alternate mechanism.
Author: Vijay Krishna
Publisher: Academic Press
ISBN: 0080922937
Category : Business & Economics
Languages : en
Pages : 337
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Book Description
Auction Theory, Second Edition improves upon his 2002 bestseller with a new chapter on package and position auctions as well as end-of-chapter questions and chapter notes. Complete proofs and new material about collusion complement Krishna’s ability to reveal the basic facts of each theory in a style that is clear, concise, and easy to follow. With the addition of a solutions manual and other teaching aids, the 2e continues to serve as the doorway to relevant theory for most students doing empirical work on auctions. Focuses on key auction types and serves as the doorway to relevant theory for those doing empirical work on auctions New chapter on combinatorial auctions and new analyses of theory-informed applications New chapter-ending exercises and problems of varying difficulties support and reinforce key points
Author: David McAdams
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
I study monotonicity of equilibrium strategies in first-price auctions with symmetric bidders, risk-aversion, affiliated types, and interdependent values. I prove that every mixed-strategy equilibrium is outcome equivalent to a monotone pure strategy equilibrium under the priority rule for breaking ties. This provides a missing link to establish uniqueness in Milgrom and Weber (1982)'s general symmetric model. Non-monotone equilibria can exist under the coin-flip rule but they are distinguishable: all non-monotone equilibria have positive probability of ties whereas all monotone equilibria have zero probability of ties. This provides a justification for the standard empirical practice of restricting attention to monotone strategies.
Author: René Kirkegaard
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We consider must-sell auctions with asymmetric buyers. First, we study auctions with two asymmetric buyers, where the distribution of valuations of the strong buyer is stretched relative to that of the weak buyer. Then, it is known that inefficient first-price auctions are more profitable for the seller than efficient second-price auctions. This is because the former favor the weak buyer. However, we show that the seller can do one better by augmenting the first-price auction by a pre-auction offer made exclusively to the strong buyer. Should the strong buyer reject the offer, the object is simply sold in an ordinary first-price auction. The result is driven by the fact that the unmodified first-price auction is too favorable to the weak buyer, and that the pre-auction offer allows some correction of this to the benefit of the seller. Secondly, we show quite generally that pre-auction offers never increase the profitability of second-price auctions, since they introduce the wrong kind of favoritism from the perspective of seller profits.
Author: Dirk Bergemann
Publisher:
ISBN:
Category : Auctions
Languages : en
Pages : 0
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Book Description
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.
