All equilibria of the multi-unit Vickrey auction

Blume, Andreas; Heidhues, Paul; Lafky, Jonathan; Münster, Johannes; Zhang, Meixia

doi:10.1016/j.geb.2008.08.002

Cited by 19 publications

(7 citation statements)

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“…Furthermore, the existence of resale markets does not guarantee the efficiency of the final outcome. Our experiment is designed to study the following: (1) Comparisons of the efficiency rates in SP and Vickrey auctions with and without resale; (2) Sources of 10 A Vickrey auction has other equilibria as shown in the literature (see Blume et al (2009)). Similarly, when resale is allowed, there are implausible equilibria.…”

Section: Methodsmentioning

confidence: 99%

“…Similarly, when resale is allowed, there are implausible equilibria. As noted in Blume et al (2009), in any equilibrium, except the value bidding equilibrium, the bidders need to coordinate on who bid zero similar to the equilibria of SPR discussed in Remark 1. efficiency losses when there are any; (3) Rankings of formats by the bidders and the seller.…”

Section: Methodsmentioning

confidence: 99%

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Multi-object auctions with resale: Theory and experiment

Filiz‐Ozbay

Lopez-Vargas

Özbay

2015

Games and Economic Behavior

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Abstract. We study multi-object auctions in the presence of post-auction trade opportunities among bidders who have either single-or multi-object demand. We focus on two formats: Vickrey auctions where package bidding is possible and simultaneous second-price auctions. We show that, under complementarities, the Vickrey format has an equilibrium where the objects are allocated efficiently at the auction stage whether resale markets are present or not. The simultaneous second-price, on the other hand, leads to inefficiency with or without resale possibility. Our experimental findings show that the possibility of resale in second-price auctions decreases the efficiency rate at the auction stage compared to the no resale case. However, after resale, the efficiency rate in second-price is as high as that of Vickrey auction without resale outcomes in the experiment.Preventing resale neither benefits nor hurts auction revenues in a second-price format. (JEL D44, C72, C91)

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Multi-object auctions with resale: Theory and experiment

Filiz‐Ozbay

Lopez-Vargas

Özbay

2015

Games and Economic Behavior

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“…[12], [13]. An auction with symmetric valuations is called a multi-unit auction and several results have been proposed in multi-unit auctions [2], [9], [11]. The auction for the super-long-term Japanese Goverment Bonds is an example of multi-unit auctions [7].…”

Section: Submodular If F I (S ∪T )+ F I (S ∩T ) ≤ F I (S )+ F I (T ) mentioning

confidence: 99%

Nash Equilibria in Combinatorial Auctions with Item Bidding by Two Bidders

Umeda

Asano

2017

Journal of Information Processing

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Abstract:We discuss Nash equilibria in combinatorial auctions with item bidding. Specifically, we give a characterization for the existence of a Nash equilibrium in such a combinatorial auction when valuations by two bidders satisfy symmetric and subadditive properties. Based on this characterization, we can obtain an algorithm for deciding whether a Nash equilibrium exists in such a combinatorial auction.Keywords: Nash equilibrium, combinatorial auction, second-price auction, subadditivity, symmetric valuation, price of anarchyIn a combinatorial auction, m items M = {1, 2, . . . , m} are offered for sale to n bidders N = {1, 2, . . . , n}. Each bidder i has a valuation f i that assigns a nonnegative real number to every subset S of M. The objective is to find a partition S 1 , S 2 , . . . , S n of M among the bidders such that the social welfareis maximized. The combinatorial auction problem is sometimes called the social welfare problem when we disregard strategic issues on bidders' selfish concerns. VCG (Vickrey-Clarke-Groves) mechanisms optimize the social welfare in a combinatorial auction with selfish bidders. However, it may take exponential time in m and n. Actually, the social welfare problem is shown to be NP-hard by Lehmann, Lehmann and Nisan, even if every val-Therefore approximation algorithms have also been proposed for the social welfare problem (in a combinatorial auction). Since each valuation f i is defined by 2 m subsets of M, most proposed approximation algorithms are based on oracle models. Two oracle models, the value queries oracle model and the demand queries oracle model, are commonly used. Furthermore, in most proposed approximation algorithms, each valuation f i is restricted to satisfy some conditions. Two restrictions, submodularity and subadditivity, are commonly used. For the submodular social welfare problem (i.e., each valuation is submodular) with the value queries oracle model, the following are known. Lehmann, Lehmann and Nisan proposed a 1 2 -approximation algorithm [12]. Khot et al. showed that this problem cannot be approximated to a factor better than 1 − asano@ise. chuo-u.ac.jp and Schapira proposed an improved (1 − 1 e )-approximation algorithm for the submodular social welfare problem [6].For the more general subadditive social welfare problem (where each valuation is subadditive), Dobzinski, Nisan, and Schapira proposed an Ω(1/ log m)-approximation algorithm using the value queries oracle model [5]. Using the more powerful demand queries oracle model, Feige proposed a 1 2 -approximation algorithm for the subadditive social welfare problem and also showed that it is NP-hard to approximate to a factor better than 1 2 [8]. He also proposed a (1 −

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“…Also, in Bertrand price competition with asymmetric costs and complete information, Erlei (2002) …nds additional equilibria. For the second-price auction, Blume and Heidhus (2004) and Blume et al (2009), show that there can be additional equilibria if one relaxes the assumption that buyers never bid above their values. We follow them by also allowing buyers in a …rst-price auction to bid above their values and (weakly) above the minimum bid.…”

Section: Modelmentioning

confidence: 99%

Multiple equilibria in asymmetric first-price auctions

Kaplan

Zamir

2014

Econ Theory Bull

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Maskin and Riley (2003) and Lebrun (2006) prove that the BayesNash equilibrium of …rst-price auctions is unique. This uniqueness requires the assumption that a buyer never bids above his value. We demonstrate that, in asymmetric …rst-price auctions (with or without a minimum bid), the relaxation of this assumption results in additional equilibria that are "substantial."Although in each of these additional equilibria no buyer wins with a bids above his value, the allocation of the object and the selling price may vary among the equilibria.Furthermore, we show that such phenomena can only occur under asymmetry in the distributions of values.JEL Codes: C72, D44.

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All equilibria of the multi-unit Vickrey auction

Cited by 19 publications

References 11 publications

Multi-object auctions with resale: Theory and experiment

Multi-object auctions with resale: Theory and experiment

Nash Equilibria in Combinatorial Auctions with Item Bidding by Two Bidders

Multiple equilibria in asymmetric first-price auctions

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