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On the properties of equilibria in private value divisible good auctions with constrained bidding

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Author Info

  • Kastl, Jakub

Abstract

I analyze a model of a private value divisible good auction with different payment rules, standard rationing rule pro-rata on-the-margin and both with and without a restriction on the number of bids (steps) bidders can submit. I provide characterization of equilibrium bidding strategies in a model with restricted strategy sets and I show that these equilibria converge to an equilibrium of the model with unrestricted strategy sets as the restrictions are relaxed. However, not all equilibria in the unrestricted game can be achieved as limits of the equilibria of the restricted games. I demonstrate that the equilibrium conditions require that the Euler condition characterizing equilibrium in continuously differentiable strategies in the unrestricted model holds “on average” over the intervals defined by the length of each (price) step of the restricted strategy, where the average is taken with respect to the endogenous distribution of the market clearing price. The characterization from the restricted model also allows for a natural interpretation of the involved trade-offs. Adapting the argument of Chao and Wilson (1987) I also prove that the foregone surplus of a bidder from using K steps rather than a continuous bid is proportional to 1K2.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 6 ()
Pages: 339-352

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Handle: RePEc:eee:mateco:v:48:y:2012:i:6:p:339-352

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Multiunit auctions; Uniform price auction; Discriminatory auction; Step functions;

References

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  1. Natalia Fabra & Nils-Henrik von der Fehr & David Harbord, 2002. "Designing Electricity Auctions," Microeconomics 0211017, EconWPA, revised 31 Aug 2003.
  2. 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.
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  4. Ilan Kremer, 2004. "Underpricing and Market Power in Uniform Price Auctions," Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 849-877.
  5. Brenner, Menachem & Galai, Dan & Sade, Orly, 2009. "Sovereign debt auctions: Uniform or discriminatory?," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 267-274, March.
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  7. LiCalzi, Marco & Pavan, Alessandro, 2005. "Tilting the supply schedule to enhance competition in uniform-price auctions," European Economic Review, Elsevier, vol. 49(1), pages 227-250, January.
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  10. McAdams, David, 2007. "Adjustable supply in uniform price auctions: Non-commitment as a strategic tool," Economics Letters, Elsevier, vol. 95(1), pages 48-53, April.
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  12. Ali Horta�su & David McAdams, 2010. "Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the Turkish Treasury Auction Market," Journal of Political Economy, University of Chicago Press, vol. 118(5), pages 833 - 865.
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  15. Jakub Kastl, 2011. "Discrete Bids and Empirical Inference in Divisible Good Auctions," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 974-1014.
  16. de Castro, Luciano I. & Riascos, Alvaro, 2009. "Characterization of bidding behavior in multi-unit auctions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 559-575, 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. Back, Kerry & Zender, Jaime F, 1993. "Auctions of Divisible Goods: On the Rationale for the Treasury Experiment," Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 733-64.
  19. Dan Levin, 2005. "Demand Reduction in Multi-Unit Auctions: Evidence from a Sportscard Field Experiment: Comment," American Economic Review, American Economic Association, vol. 95(1), pages 467-471, March.
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  21. Lawrence M. Ausubel & Peter Cramton, 1995. "Demand Reduction and Inefficiency in Multi-Unit Auctions," Papers of Peter Cramton 98wpdr, University of Maryland, Department of Economics - Peter Cramton, revised 22 Jul 2002.
  22. David Lucking-Reiley & John A. List, 2000. "Demand Reduction in Multiunit Auctions: Evidence from a Sportscard Field Experiment," American Economic Review, American Economic Association, vol. 90(4), pages 961-972, September.
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  24. Green, Richard & Newbery, David M G, 1991. "Competition in the British Electricity Spot Market," CEPR Discussion Papers 557, C.E.P.R. Discussion Papers.
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Citations

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Cited by:
  1. Nuno Cassola & Ali Hortacsu & Jakub Kastl, 2009. "The 2007 Subprime Market Crisis Through the Lens of European Central Bank Auctions for Short-Term Funds," Discussion Papers 08-039, Stanford Institute for Economic Policy Research.
  2. Zulehner, Christine & Elsinger, Helmut & Schmidt-Dengler, Philipp, 2013. "Competition in Austrian Treasury Auctions," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79963, Verein für Socialpolitik / German Economic Association.
  3. Ali Hortacsu & Jakub Kastl, 2008. "Testing for Common Values in Canadian Treasury Bill Auctions," Discussion Papers 07-053, Stanford Institute for Economic Policy Research.
  4. Romans Pancs, 2014. "Workup," Review of Economic Design, Springer, vol. 18(1), pages 37-71, March.
  5. Holmberg, P. & Newbery, D & Ralph, D., 2008. "Supply Function Equilibria: Step Functions and Continuous Representations," Cambridge Working Papers in Economics 0863, Faculty of Economics, University of Cambridge.
  6. de Frutos, María-Ángeles & Fabra, Natalia, 2012. "How to allocate forward contracts: The case of electricity markets," European Economic Review, Elsevier, vol. 56(3), pages 451-469.
  7. Hortaçsu, Ali, 2011. "Recent progress in the empirical analysis of multi-unit auctions," International Journal of Industrial Organization, Elsevier, vol. 29(3), pages 345-349, May.
  8. Mar Reguant, 2014. "Complementary Bidding Mechanisms and Startup Costs in Electricity Markets," CESifo Working Paper Series 4811, CESifo Group Munich.

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