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Affiliation, equilibrium existence and the revenue ranking of auctions

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  • Luciano I. de Castro

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Abstract

We consider private value auctions where bidders’ types are dependent, a case usually treated by assuming affiliation. We show that affiliation is a restrictive assumption in three senses: topological, measure-theoretic and statistical (affiliation is a very restrictive characterization of positive dependence). We also show that affiliation’s main implications do not generalize for alternative definitions of positive dependence. From this, we propose new approaches to the problems of pure strategy equilibrium existence in first-price auctions (PSEE) and the characterization of the revenue ranking of auctions. For equilibrium existence, we slightly restrict the set of distributions considered, without loss of economic generality, and offer a complete characterization of PSEE. For revenue ranking, we obtain a characterization of the expected revenue differences between second and first price auctions with general dependence of types.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we074622.

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Date of creation: May 2007
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Handle: RePEc:cte:werepe:we074622

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References

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  1. Engelbrecht-Wiggans, Richard & Milgrom, Paul R. & Weber, Robert J., 1983. "Competitive bidding and proprietary information," Journal of Mathematical Economics, Elsevier, vol. 11(2), pages 161-169, April.
  2. Athey,S. & Haile,P.A., 2000. "Identification of standard auction models," Working papers 13, Wisconsin Madison - Social Systems.
  3. Jackson, Matthew O. & Jeroen Swinkels, 2004. "Existence of Equilibrium in Single and Double Private Value Auctions," Working Papers 1192, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
  5. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. 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.
  7. Milgrom, Paul, 1989. "Auctions and Bidding: A Primer," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 3-22, Summer.
  8. Robert B. Wilson, 1967. "Competitive Bidding with Asymmetric Information," Management Science, INFORMS, vol. 13(11), pages 816-820, July.
  9. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
  10. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
  11. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  12. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-43, June.
  13. Klemperer, Paul, 2003. "Using and Abusing Economic Theory," CEPR Discussion Papers 3813, C.E.P.R. Discussion Papers.
  14. Milgrom, Paul & Weber, Robert J., 1982. "The value of information in a sealed-bid auction," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 105-114, June.
  15. Monteiro, Paulo Klinger & Moreira, Humberto, 2006. "First-price auctions without affiliation," Economics Letters, Elsevier, vol. 91(1), pages 1-7, April.
  16. repec:wop:humbsf:2000-72 is not listed on IDEAS
  17. Motty Perry & Philip J. Reny, 1999. "On The Failure of the Linkage Principle in Multi-Unit Auctions," Econometrica, Econometric Society, vol. 67(4), pages 895-900, July.
  18. Wilson, Robert, 1977. "A Bidding Model of Perfect Competition," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 511-18, October.
  19. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
  20. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
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Citations

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Cited by:
  1. Gresik, Thomas A., 2011. "The effects of statistically dependent values on equilibrium strategies of bilateral k-double auctions," Games and Economic Behavior, Elsevier, vol. 72(1), pages 139-148, May.
  2. Luciano I. de Castro, 2009. "Affiliation and Dependence in Economic Models," Discussion Papers 1479, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Luciano De Castro, 2012. "Correlation of Types in Bayesian Games," Discussion Papers 1556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Gino Loyola, 2008. "On bidding markets: the role of competition," Economics Working Papers we083318, Universidad Carlos III, Departamento de Economía.
  5. Hubbard, Timothy P. & Li, Tong & Paarsch, Harry J., 2011. "Semiparametric Estimation in Models of First-Price, Sealed-Bid Auctions with Affiliation," CEI Working Paper Series 2010-10, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
  6. Luciano De Castro, 2010. "Affiliation, Equilibrium Existence and Revenue Ranking of Auctions," Discussion Papers 1530, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Olivier Compte & Andrew Postlewaite, 2010. "Simple Auctions, Second Version," PIER Working Paper Archive 13-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Apr 2013.
  8. Yuanyuan Wan & Haiqing Xu, 2010. "Semiparametric identification and estimation of binary discrete games of incomplete information with correlated private signals," Department of Economics Working Papers 130913, The University of Texas at Austin, Department of Economics.
  9. Maciej H. Kotowski & Fei Li, 2012. "On the Continuous Equilibria of Affiliated-Value, All-Pay Auctions with Private Budget Constraints," PIER Working Paper Archive 12-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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