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Existence of Equilibrium in Single and Double Private Value Auctions

Jackson, Matthew O. and Swinkels, Jeroen M. (2004) Existence of Equilibrium in Single and Double Private Value Auctions. Social Science Working Paper, 1192. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170731-142826926

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Abstract

We show existence of equilibria in distributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of equilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard pricing rules, reserve prices, entry costs, and stochastic demand and supply. Valuations can be correlated and asymmetrically distributed. For double auctions, we show further that at least one equilibrium involves a positive volume of trade. The existence proof establishes new connections among existence techniques for discontinuous Bayesian games.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:JACe05Related ItemPublished Version
ORCID:
AuthorORCID
Jackson, Matthew O.0000-0001-9846-4249
Additional Information:We thank Leo Simon, Bill Zame, Mark Satterthwaite and Phil Reny for helpful conversations. We also thank Kim Border, Martin Cripps, John Nachbar, Andy Postlewaite, Larry Samuelson, Tianxiang Ye, three anonymous referees and the editor for helpful comments and suggestions. Financial support from the National Science Foundation under grant SES-9986190 and from the Boeing Center for Technology and Information Management is gratefully acknowledged. This paper supersedes the second part of Jackson and Swinkels [1]. That paper was split: The results on existence of equilibria in Bayesian games with type-dependent sharing were combined with Simon and Zame [2] to become Jackson, Simon, Swinkels, and Zame [3]. The results on existence of equilibria in a class of private value auctions have evolved into this paper. Published as Jackson, M.O., & Swinkels, J.M. (2005). Existence of equilibrium in single and double private value auctions. Econometrica, 73(1), 93-139. [1]Jackson, M.O. and J.M. Swinkels (1999) "Existence of Equilibrium in Auctions and Discontinuous Bayesian Games: Endogenous and Incentive Compatible Sharing Rules," mimeo, Caltech. [2]Simon, L.K. and W.R. Zame (1999): "Cheap Talk and Discontinuous Games of Incomplete Information." UCLA Working Paper. [3]Jackson, M.O., L.K. Simon, J.M. Swinkels, and W.R. Zame (2002): "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, 70(5), 1711-1740.
Group:Social Science Working Papers
Funders:
Funding AgencyGrant Number
NSFSES-9986190
Boeing Center for Technology and Information ManagementUNSPECIFIED
Subject Keywords:Auctions, Double Auctions, Equilibrium, Existence, Invariance, Private Values
Series Name:Social Science Working Paper
Issue or Number:1192
Classification Code:JEL: C62,C63,D44,D82
Record Number:CaltechAUTHORS:20170731-142826926
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170731-142826926
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79615
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:01 Aug 2017 23:03
Last Modified:03 Oct 2019 18:22

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