Correlation of Types in Bayesian Games
Despite their importance, games with incomplete information and dependent types are poorly understood; only special cases have been considered and a general approach is not yet available. In this paper, we propose a new condition (named richness) for correlation of types in (asymmetric) Bayesian games. Richness is related to the idea that “beliefs do not determine preferences” and that types should be modeled with two explicit parts: one for payoffs and another for beliefs. With this condition, we are able to provide the first pure strategy equilibrium existence result for a general model of multi-unit auctions with correlated types. We then focus on a special case of richness, called “grid distributions,” and establish necessary and sufficient conditions for the existence of a symmetric monotonic pure strategy equilibrium in first-price auctions with general levels of correlation. We also provide a polynomial-time algorithm to verify this existence and suggest, using simulations, that the revenue superiority of English auctions may not hold for positively correlated types in general. JEL Classification Numbers: C62, C72, D44, D82
|Date of creation:||01 Jul 2012|
|Date of revision:|
|Contact details of provider:|| Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014|
Web page: http://www.kellogg.northwestern.edu/research/math/
More information through EDIRC
|Order Information:|| Email: |
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.:
- Hanming Fang & Stephen Morris, 2003.
"Multidimensional Private Value Auctions,"
Cowles Foundation Discussion Papers
1423, Cowles Foundation for Research in Economics, Yale University.
- Hanming Fang, 2004. "Multidimensional Private Value Auctions," Theory workshop papers 121473000000000021, UCLA Department of Economics.
- Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Econometric Society 2004 North American Winter Meetings 174, Econometric Society.
- Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Yale School of Management Working Papers ysm387, Yale School of Management.
- Castro, Luciano I. De & Paarsch, Harry J., 2009. "Testing Affiliation in Private-values Models of First-price Auctions Using Grid Distributions," CEI Working Paper Series 2009-11, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
- Castro, Luciano I. de, 2007. "Affiliation, equilibrium existence and the revenue ranking of auctions," UC3M Working papers. Economics we074622, Universidad Carlos III de Madrid. Departamento de Economía.
- Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
- Robert Wilson, 1977. "A Bidding Model of Perfect Competition," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 511-518.
- 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.
- John K.-H. Quah & Bruno Strulovici, 2007.
"Comparative Statics, Informativeness, and the Interval Dominance Order,"
2007-W04, Economics Group, Nuffield College, University of Oxford.
- John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
- Aviad Heifetz & Dov Samet, 1996.
"Topology-Free Typology of Beliefs,"
Game Theory and Information
9609002, EconWPA, revised 17 Sep 1996.
- Aviad Heifetz & Zvika Neeman, 2006.
"On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design,"
Econometric Society, vol. 74(1), pages 213-233, 01.
- Aviad Heifetz & Zvika Neeman, 2004. "On the Generic (Im)possibility of Full Surplus Extraction in Mechanism Design," Discussion Paper Series dp350, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Van Zandt, Timothy, 2010. "Interim Bayesian Nash equilibrium on universal type spaces for supermodular games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 249-263, January.
- McAdams, David, 2007. "On the failure of monotonicity in uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 137(1), pages 729-732, November.
- Van Zandt, Timothy & Vives, Xavier, 2007.
"Monotone equilibria in Bayesian games of strategic complementarities,"
Journal of Economic Theory,
Elsevier, vol. 134(1), pages 339-360, May.
- Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers.
- Jackson, Matthew O., 2005.
"Non-Existence of Equilibrium in Vickrey, Second-Price, and English Auctions,"
1241, California Institute of Technology, Division of the Humanities and Social Sciences.
- Matthew Jackson, 2009. "Non-existence of equilibrium in Vickrey, second-price, and English auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 13(1), pages 137-145, April.
- Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
- David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
- Ilan Kremer & Kjell G. Nyborg, 2004. "Divisible-Good Auctions: The Role of Allocation Rules," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 147-159, Spring.
- Monteiro, Paulo Klinger & Moreira, Humberto, 2006. "First-price auctions without affiliation," Economics Letters, Elsevier, vol. 91(1), pages 1-7, April.
- Rustichini, Aldo, 1993. "Mixing on Function Spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 183-91, January.
- Castro, Luciano I. de & Araujo, Aloisio, 2006.
"Pure strategy equilibria of single and double auctions with interdependent values,"
UC3M Working papers. Economics
we065320, Universidad Carlos III de Madrid. Departamento de Economía.
- Araujo, Aloisio & de Castro, Luciano I., 2009. "Pure strategy equilibria of single and double auctions with interdependent values," Games and Economic Behavior, Elsevier, vol. 65(1), pages 25-48, January.
- Neeman, Zvika, 2004.
"The relevance of private information in mechanism design,"
Journal of Economic Theory,
Elsevier, vol. 117(1), pages 55-77, July.
- Zvika Neeman, 1998. "The Relevance of Private Information in Mechanism Design," Papers 0093, Boston University - Industry Studies Programme.
- Neeman, Z., 1998. "The Relevance of Private Infromation in Mechanism Design," Papers 93, Boston University - Department of Economics.
- Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, 03.
- William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
When requesting a correction, please mention this item's handle: RePEc:nwu:cmsems:1556. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fran Walker)
If references are entirely missing, you can add them using this form.