On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions

This file is part of IDEAS, which uses RePEc data

On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions

Author Info

Philip J. Reny ()
Shmuel Zamir ()

Additional information is available for the following registered author(s):

Philip J. Reny

Abstract

We establish the existence of pure strategy equilibria in monotone bidding functions in first-price auctions with asymmetric bidders, interdependent values and affiliated one-dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second-price auctions.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

Publisher Info
Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp292.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 28 pages
Date of creation: Jun 2002
Date of revision:
Publication status: Published in Econometrica, 2004, vol. 72, pp. 1105-1125.
Handle: RePEc:huj:dispap:dp292

Contact details of provider:
Postal: Feldman Building - Givat Ram - 91904 Jerusalem
Phone: +972-2-6584135
Fax: +972-2-6513681
Email:
Web page: http://www.ratio.huji.ac.il/
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Ron Peretz).

Other versions of this item:

Article
- Philip J. Reny & Shmuel Zamir, 2004. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Econometric Society, vol. 72(4), pages 1105-1125, 07. [Downloadable!] (restricted)

This paper has been announced in the following NEP Reports:

NEP-ALL-2003-05-15 (All new papers)
NEP-GTH-2003-05-15 (Game Theory)
NEP-IND-2003-05-15 (Industrial Organization)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Eric Maskin & John Riley, 2003. "Uniqueness of Equilibrium in Sealed High-Bid Auctions," Economics Working Papers 0031, Institute for Advanced Study, School of Social Science. [Downloadable!]
Other versions:
- Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November. [Downloadable!] (restricted)
Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 439-54, July.
Gustavo E. Rodriguez, 2000. "First price auctions: Monotonicity and uniqueness," International Journal of Game Theory, Springer, vol. 29(3), pages 413-432. [Downloadable!] (restricted)
Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
Other versions:
- Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September. [Downloadable!] (restricted)
Other versions:
- Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January. [Downloadable!] (restricted)

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Sudip Gupta, 2004. "Endogenous Asymmetry and Entry in Sequential Multi-Unit Auctions: Identification and Estimation," Econometric Society 2004 North American Summer Meetings 566, Econometric Society. [Downloadable!]
Aloisio Araujo & Luciano I. de Castro & Humberto Moreira, 2006. "Non-Monotoniticies And The All-Pay Auction Tie-Breaking Rule," Economics Working Papers we065924, Universidad Carlos III, Departamento de Economía. [Downloadable!]
Aloisio Araujo & Luciano I. de Castro, 2006. "Pure Strategy Equilibria Of Single And Double Auctions With Interdependent Values," Economics Working Papers we065320, Universidad Carlos III, Departamento de Economía. [Downloadable!]
John Asker & Estelle Cantillon, 2004. "Equilibrium in Scoring Auctions," Working Papers 2004.148, Fondazione Eni Enrico Mattei. [Downloadable!]
McAdams, David, 2002. "Bidding Lower with Higher Values in Multi-Object Auction," Working papers 4249-02, Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
Philip J. Reny, 2005. "On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games," Levine's Working Paper Archive 784828000000000067, David K. Levine. [Downloadable!]
Other versions:
- Philip J Reny, 2005. "On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games," NajEcon Working Paper Reviews 784828000000000413, www.najecon.org. [Downloadable!]
- Philip J Reny, 2005. "On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games," Levine's Working Paper Archive 784828000000000413, David K. Levine. [Downloadable!]
Moreira, Humberto Luiz Ataide & Araújo, Aloísio Pessoa de & Castro Filho, Luciano I. de Castro Filho, 2004. "Pure strategy equilibria of multidimensional and Non-monotonic auctions," Economics Working Papers (Ensaios Economicos da EPGE) 571, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
Mason, Robin & Valentinyi, Akos, 2004. "Independence and Heterogeneity in Games of Incomplete Information," CEPR Discussion Papers 4177, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
Other versions:
- Mason, Robin & Valentinyi, Ãkos, 2003. "Independence And Heterogeneity In Games Of Incomplete Information," Discussion Paper Series In Economics And Econometrics 0307, Economics Division, School of Social Sciences, University of Southampton. [Downloadable!]
Hanming Fang & Stephen Morris, 2003. "Multidimensional Private Value Auctions," Cowles Foundation Discussion Papers 1423, Cowles Foundation, Yale University. [Downloadable!]
Other versions:
- Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Econometric Society 2004 North American Winter Meetings 174, Econometric Society. [Downloadable!]
- Hanming Fang, 2004. "Multidimensional Private Value Auctions," Theory workshop papers 121473000000000021, UCLA Department of Economics. [Downloadable!]
- Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Yale School of Management Working Papers ysm387, Yale School of Management. [Downloadable!]
- Fang, Hanming & Morris, Stephen, 2006. "Multidimensional private value auctions," Journal of Economic Theory, Elsevier, vol. 126(1), pages 1-30, January. [Downloadable!] (restricted)
Luciano I. de Castro, 2007. "Affiliation, equilibrium existence and the revenue ranking of auctions," Economics Working Papers we074622, Universidad Carlos III, Departamento de Economía. [Downloadable!]
Aloisio Araujo & Luciano Castro & Humberto Moreira, 2008. "Non-monotoniticies and the all-pay auction tie-breaking rule," Economic Theory, Springer, vol. 35(3), pages 407-440, June. [Downloadable!] (restricted)
Olivier Armantier & Jean-Pierre Florens & Jean-Francois Richard, 2008. "Approximation of Nash equilibria in Bayesian games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 965-981. [Downloadable!]
Eric Maskin & John Riley, 2003. "Uniqueness of Equilibrium in Sealed High-Bid Auctions," Economics Working Papers 0031, Institute for Advanced Study, School of Social Science. [Downloadable!]
Other versions:
- Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November. [Downloadable!] (restricted)
Aloisio Araujo & Luciano I. de Castro Filho, 2004. "Pure Strategy Equilibria of Multidimensional and Non-Monotonic Auctions," Econometric Society 2004 Latin American Meetings 300, Econometric Society. [Downloadable!]
In-Koo Cho, 2004. "Monotonicity and Rationalizability in Large Uniform Price and Double Auctions," Theory workshop papers 658612000000000076, UCLA Department of Economics. [Downloadable!]
Gatti, J.R.J., 2005. "A Note on the Existence of Nash Equilibrium in Games with Discontinuous Payoffs," Cambridge Working Papers in Economics 0510, Faculty of Economics, University of Cambridge. [Downloadable!]
Shmuel Zamir, 2008. "Bayesian games: games of incomplete information," Levine's Bibliography 122247000000002215, UCLA Department of Economics. [Downloadable!]

Statistics

Access and download statistics

Did you know? RePEc stands for Research Papers in Economics.

This page was last updated on 2009-11-22.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.