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Non-monotoniticies and the all-pay auction tie-breaking rule

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  • Aloisio Araujo

    ()

  • Luciano Castro

    ()

  • Humberto Moreira

    ()

Abstract

Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The best results available ensure equilibrium existence only in mixed strategy with endogenously defined tie-breaking rules and communication of private information. We show that an all-pay auction tie-breaking rule is sufficient for the existence of pure strategy equilibrium in a class of auctions. The rule is explicitly defined and does not require communication of private information. We also characterize when special tie-breaking rules are really needed.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 35 (2008)
Issue (Month): 3 (June)
Pages: 407-440

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Handle: RePEc:spr:joecth:v:35:y:2008:i:3:p:407-440

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Related research

Keywords: Auctions; Pure strategy equilibria; Non-monotonic bidding functions; Tie-breaking rules; Necessary and sufficient conditions for equilibrium; Multidimensional types; C62; C72; D44; D82;

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References

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  1. Susan Athey & Jonathan Levin, 1999. "Information and Competition in U.S. Forest Service Timber Auctions," Working papers 99-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Ewerhart II, Christian & Fieseler, Karsten, 2002. "Procurement Auctions and Unit-Price Contracts," Sonderforschungsbereich 504 Publications 02-11, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  3. 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.
  4. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
  5. Araújo, Aloísio Pessoa de & Moreira, Humberto Ataíde, 2001. "Adverse Selection Problems without The Spence-Mirrlees Condition," Economics Working Papers (Ensaios Economicos da EPGE) 425, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  6. Zheng, Charles Z., 2001. "High Bids and Broke Winners," Journal of Economic Theory, Elsevier, vol. 100(1), pages 129-171, September.
  7. 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.
  8. Araújo, Aloísio Pessoa de & Moreira, Humberto Ataíde, 2003. "Non-Monotone insurance contracts and their empirical consequences," Economics Working Papers (Ensaios Economicos da EPGE) 512, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  9. 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.
  10. 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.
  11. 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.
  12. Monteiro, Paulo Klinger, 2009. "First-price auction symmetric equilibria with a general distribution," Games and Economic Behavior, Elsevier, vol. 65(1), pages 256-269, January.
  13. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  14. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
  15. P. Dasgupta & Eric Maskin, 1998. "Efficient Auctions," Harvard Institute of Economic Research Working Papers 1857, Harvard - Institute of Economic Research.
  16. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-90, September.
  17. 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.
  18. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
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  20. 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.
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Citations

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Cited by:
  1. Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Subhashish Modak Chowdhury, 2009. "The all-pay auction with non-monotonic payoff," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-09, School of Economics, University of East Anglia, Norwich, UK..
  3. Luciano Castro, 2011. "Equilibrium existence and approximation of regular discontinuous games," Economic Theory, Springer, vol. 48(1), pages 67-85, September.

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