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Pure Strategy Equilibria Of Single And Double Auctions With Interdependent Values

  • Aloisio Araujo
  • Luciano I. de Castro

    ()

We prove the existence of monotonic pure strategy equilibrium for many types of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidder's type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present a reasonable counterexample for interdependent values auctions that shows that sometimes all equilibria are trivial, that is, they have zero probability of trade. Nevertheless, we give sufficient conditions for non-trivial equilibrium existence.

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we065320.

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Date of creation: Aug 2006
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Handle: RePEc:cte:werepe:we065320
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  1. 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.
  2. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
  3. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  6. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  7. Akerlof, George A, 1970. "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, MIT Press, vol. 84(3), pages 488-500, August.
  8. Fudenberg, Drew & Mobius, Markus & Szeidl, Adam, 2010. "Existence of Equilibrium in Large Double Auctions," Staff General Research Papers 32111, Iowa State University, Department of Economics.
  9. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
  10. Simon, Leo K. & Zame, William R., 1987. "Discontinous Games and Endogenous Sharing Rules," Department of Economics, Working Paper Series qt8n46v2wv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  11. 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.
  12. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  13. Moreira, Humberto Ataíde & 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, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  14. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
  15. 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.
  16. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-43, June.
  17. Philip J Reny & Motty Perry, 2006. "Toward a Strategic Foundation for Rational Expectations Equilibrium," Econometrica, Econometric Society, vol. 74(5), pages 1231-1269, 09.
  18. Luciano I. De Castro & Alvaro Riascos, 2007. "Characterization of Bidding Behavior in Multi-Unit," DOCUMENTOS CEDE 004382, UNIVERSIDAD DE LOS ANDES-CEDE.
  19. 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.
  20. Williams, Steven R, 1991. "Existence and Convergence of Equilibria in the Buyer's Bid Double Auction," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 351-74, April.
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