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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. Paul Klemperer, 2003. "Using and Abusing Economic Theory," Economics Series Working Papers 2003-W02, University of Oxford, Department of Economics.
  2. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  3. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
  4. Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, 01.
  5. Milgrom, Paul, 1989. "Auctions and Bidding: A Primer," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 3-22, Summer.
  6. 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.
  7. 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.
  8. Monteiro, Paulo Klinger & Moreira, Humberto, 2006. "First-price auctions without affiliation," Economics Letters, Elsevier, vol. 91(1), pages 1-7, April.
  9. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November.
  10. 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.
  11. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. repec:wop:humbsf:2000-72 is not listed on IDEAS
  13. Robert B. Wilson, 1967. "Competitive Bidding with Asymmetric Information," Management Science, INFORMS, vol. 13(11), pages 816-820, July.
  14. Paul R. Milgrom, 1979. "Good Nevs and Bad News: Representation Theorems and Applications," Discussion Papers 407R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. 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.
  16. 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.
  17. 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.
  18. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  19. Wilson, Robert, 1977. "A Bidding Model of Perfect Competition," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 511-18, October.
  20. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-43, June.
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Citations

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Cited by:
  1. 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.
  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, 2010. "Affiliation, Equilibrium Existence and Revenue Ranking of Auctions," Discussion Papers 1530, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Hubbard, Timothy P. & Li, Tong & Paarsch, Harry J., 2012. "Semiparametric estimation in models of first-price, sealed-bid auctions with affiliation," Journal of Econometrics, Elsevier, vol. 168(1), pages 4-16.
  5. 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.
  6. 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.
  7. 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.
  8. Gino Loyola, 2008. "On bidding markets: the role of competition," Economics Working Papers we083318, Universidad Carlos III, Departamento de Economía.
  9. Luciano De Castro, 2012. "Correlation of Types in Bayesian Games," Discussion Papers 1556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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