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Auctions of Homogeneous Goods: A Case for Pay-as-Bid

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  • Pycia, Marek
  • Woodward, Kyle
Abstract
The pay-as-bid (or discriminatory) auction is a prominent format for selling homogenous goods such as treasury securities and commodities. We prove the uniqueness of its pure-strategy Bayesian Nash equilibrium and establish a tractable representation of equilibrium bids. Building on these results we analyze the optimal design of pay-as-bid auctions, as well as uniform-price auctions (the main alternative auction format), allowing for asymmetric information. We show that supply transparency and full disclosure are optimal in pay-as-bid, though not necessarily in uniform-price; pay-as-bid is revenue dominant and might be welfare dominant; and, under assumptions commonly imposed in empirical work, the two formats are revenue and welfare equivalent.

Suggested Citation

  • Pycia, Marek & Woodward, Kyle, 2021. "Auctions of Homogeneous Goods: A Case for Pay-as-Bid," CEPR Discussion Papers 15656, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:15656
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    as
    1. Natalia Fabra & Nils‐Henrik Fehr & David Harbord, 2006. "Designing electricity auctions," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 23-46, March.
    2. Burkett, Justin & Woodward, Kyle, 2020. "Reserve prices eliminate low revenue equilibria in uniform price auctions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 297-306.
    3. Xavier Vives, 2010. "Asset Auctions, Information, and Liquidity," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 467-477, 04-05.
    4. Sara Castellanos & Marco Oviedo, 2008. "Optimal Bidding in the Mexican Treasury Securities Primary Auctions: Results of a Structural Econometric Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 45(131), pages 3-28.
    5. Ali Hortaçsu & Jakub Kastl & Allen Zhang, 2018. "Bid Shading and Bidder Surplus in the US Treasury Auction System," American Economic Review, American Economic Association, vol. 108(1), pages 147-169, January.
    6. Pär Holmberg, 2009. "Supply function equilibria of pay-as-bid auctions," Journal of Regulatory Economics, Springer, vol. 36(2), pages 154-177, October.
    7. Bergemann, Dirk & Pesendorfer, Martin, 2007. "Information structures in optimal auctions," Journal of Economic Theory, Elsevier, vol. 137(1), pages 580-609, November.
    8. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2019. "Revenue Guarantee Equivalence," American Economic Review, American Economic Association, vol. 109(5), pages 1911-1929, May.
    9. Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
    10. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    11. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 267-289.
    12. Ewerhart, Christian & Cassola, Nuno & Valla, Natacha, 2010. "Declining valuations and equilibrium bidding in central bank refinancing operations," International Journal of Industrial Organization, Elsevier, vol. 28(1), pages 30-43, January.
    13. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    14. repec:adr:anecst:y:2009:i:93-94:p:06 is not listed on IDEAS
    15. 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, January.
    16. Federico, Giulio & Rahman, David, 2003. "Bidding in an Electricity Pay-as-Bid Auction," Journal of Regulatory Economics, Springer, vol. 24(2), pages 175-211, September.
    17. 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.
    18. Edward J. Anderson & Pär Holmberg & Andrew B. Philpott, 2013. "Mixed strategies in discriminatory divisible-good auctions," RAND Journal of Economics, RAND Corporation, vol. 44(1), pages 1-32, March.
    19. Swinkels, Jeroen M, 2001. "Efficiency of Large Private Value Auctions," Econometrica, Econometric Society, vol. 69(1), pages 37-68, January.
    20. Manelli, Alejandro M. & Vincent, Daniel R., 2006. "Bundling as an optimal selling mechanism for a multiple-good monopolist," Journal of Economic Theory, Elsevier, vol. 127(1), pages 1-35, March.
    21. Jaime F. Zender & James J.D. Wang, 2002. "Auctioning divisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 673-705.
    22. Raymond Deneckere & James Peck, 2012. "Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting," Econometrica, Econometric Society, vol. 80(3), pages 1185-1247, May.
    23. Richard Engelbrecht‐Wiggans & Charles M. Kahn, 2002. "Multiunit Auctions in Which Almost Every Bid Wins," Southern Economic Journal, John Wiley & Sons, vol. 68(3), pages 617-631, January.
    24. Philippe Février & Raphaële Preget & Michael Visser, 2002. "Econometrics of Share Auctions," Working Papers 2002-09, Center for Research in Economics and Statistics.
    25. Richard Engelbrecht-Wiggans & Charles M. Kahn, 2002. "Multiunit Auctions in Which Almost Every Bid Wins," Southern Economic Journal, John Wiley & Sons, vol. 68(3), pages 617-631, January.
    26. Glosten, Lawrence R, 1994. "Is the Electronic Open Limit Order Book Inevitable?," Journal of Finance, American Finance Association, vol. 49(4), pages 1127-1161, September.
    27. Ahmed Anwar, 1999. "The Case for a Discriminatory Pricing Rule in Competitive Electricity Pools," Edinburgh School of Economics Discussion Paper Series 39, Edinburgh School of Economics, University of Edinburgh.
    28. 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.
    29. Olivier Armantier & Nourredine Lafhel, 2009. "Comparison of Auction Formats in Canadian Government Auctions," Staff Working Papers 09-5, Bank of Canada.
    30. Luiz T. A. Maurer & Luiz A. Barroso, 2011. "Electricity Auctions : An Overview of Efficient Practices," World Bank Publications - Books, The World Bank Group, number 2346.
    31. 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, July.
    32. Erwann SbaÏ & Olivier Armantier, 2006. "Estimation and comparison of treasury auction formats when bidders are asymmetric," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 745-779.
    33. Fang, Hanming & Parreiras, Sergio O., 2003. "On the failure of the linkage principle with financially constrained bidders," Journal of Economic Theory, Elsevier, vol. 110(2), pages 374-392, June.
    34. 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.
    35. 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.
    36. Yi‐Chun Chen & Wei He & Jiangtao Li & Yeneng Sun, 2019. "Equivalence of Stochastic and Deterministic Mechanisms," Econometrica, Econometric Society, vol. 87(4), pages 1367-1390, July.
    37. Eduardo Anthony G. Marino III & Daniel Marszalec, 2020. "Auction Performance, Strategic Supply Management, and Bidder Behavior in Treasury Bill Auctions: Evidence from the Philippines," CIRJE F-Series CIRJE-F-1138, CIRJE, Faculty of Economics, University of Tokyo.
    38. 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.
    39. Marszalec, Daniel, 2017. "The impact of auction choice on revenue in treasury bill auctions – An empirical evaluation," International Journal of Industrial Organization, Elsevier, vol. 53(C), pages 215-239.
    40. Hao Li & Xianwen Shi, 2017. "Discriminatory Information Disclosure," American Economic Review, American Economic Association, vol. 107(11), pages 3363-3385, November.
    41. Ali Hortaçsu & Jakub Kastl, 2012. "Valuing Dealers' Informational Advantage: A Study of Canadian Treasury Auctions," Econometrica, Econometric Society, vol. 80(6), pages 2511-2542, November.
    42. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    43. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    44. 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.
    45. Jeroen M. Swinkels, 1999. "Asymptotic Efficiency for Discriminatory Private Value Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 509-528.
    46. Robert Wilson, 1979. "Auctions of Shares," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(4), pages 675-689.
    47. Matthew O. Jackson & Ilan Kremer, 2006. "The Relevance of a Choice of Auction Format in a Competitive Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 961-981.
    48. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1039-1056.
    49. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
    50. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    51. Ali Hortaçsu & 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.
    52. Andreas Hefti & Peiyao Shen & Regina Betz, 2019. "Market power and information effects in a multi-unit auction," ECON - Working Papers 320, Department of Economics - University of Zurich.
    53. Boo‐Sung Kang & Steven L. Puller, 2008. "The Effect Of Auction Format On Efficiency And Revenue In Divisible Goods Auctions: A Test Using Korean Treasury Auctions," Journal of Industrial Economics, Wiley Blackwell, vol. 56(2), pages 290-332, June.
    54. Umlauf, Steven R., 1993. "An empirical study of the Mexican Treasury bill auction," Journal of Financial Economics, Elsevier, vol. 33(3), pages 313-340, June.
    55. McAdams, David, 2002. "Bidding Lower with Higher Values in Multi-Object Auction," Working papers 4249-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    56. Simon Board, 2009. "Revealing information in auctions: the allocation effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 125-135, January.
    57. Ilan Kremer, 2004. "Underpricing and Market Power in Uniform Price Auctions," The Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 849-877.
    58. 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 861-889, July.
    59. Grossman, S J & Hart, O D, 1980. "Disclosure Laws and Takeover Bids," Journal of Finance, American Finance Association, vol. 35(2), pages 323-334, May.
    60. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    61. Alessandro Pavan & Ilya Segal & Juuso Toikka, 2014. "Dynamic Mechanism Design: A Myersonian Approach," Econometrica, Econometric Society, vol. 82(2), pages 601-653, March.
    62. Olivier Armantier & Jean-Pierre Florens & Jean-Francois Richard, 2008. "Approximation of Nash equilibria in Bayesian games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 965-981.
    63. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    64. Kastl, Jakub, 2012. "On the properties of equilibria in private value divisible good auctions with constrained bidding," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 339-352.
    65. Back, Kerry & Zender, Jaime F, 1993. "Auctions of Divisible Goods: On the Rationale for the Treasury Experiment," The Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 733-764.
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    Cited by:

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