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

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  • 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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:6:p:339-352
    DOI: 10.1016/j.jmateco.2012.07.006
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    4. Anderson, Edward & Holmberg, Pär, 2018. "Price instability in multi-unit auctions," Journal of Economic Theory, Elsevier, vol. 175(C), pages 318-341.
    5. Pär Holmberg, 2017. "Pro‐competitive Rationing in Multi‐unit Auctions," Economic Journal, Royal Economic Society, vol. 127(605), pages 372-395, October.
    6. Mar Reguant, 2014. "Complementary Bidding Mechanisms and Startup Costs in Electricity Markets," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1708-1742.
    7. Romans Pancs, 2014. "Workup," Review of Economic Design, Springer;Society for Economic Design, vol. 18(1), pages 37-71, March.
    8. Pär Holmberg & Frank Wolak, 2015. "Electricity markets: Designing auctions where suppliers have uncertain costs," Working Papers EPRG 1523, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    9. Wittwer, Milena, 2017. "Centralizing Disconnected Markets? An Irrelevance Result," MPRA Paper 76534, University Library of Munich, Germany.
    10. Zulehner, Christine & Elsinger, Helmut & Schmidt-Dengler, Philipp, 2013. "Competition in Austrian Treasury Auctions," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79963, Verein für Socialpolitik / German Economic Association.
    11. Fiuza de Bragança, Gabriel Godofredo & Daglish, Toby, 2016. "Can market power in the electricity spot market translate into market power in the hedge market?," Energy Economics, Elsevier, vol. 58(C), pages 11-26.
    12. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    13. Nuno Cassola & Ali Hortaçsu & Jakub Kastl, 2013. "The 2007 Subprime Market Crisis Through the Lens of European Central Bank Auctions for Short‐Term Funds," Econometrica, Econometric Society, vol. 81(4), pages 1309-1345, July.
    14. Bustos-Salvagno, Javier, 2015. "Bidding behavior in the Chilean electricity market," Energy Economics, Elsevier, vol. 51(C), pages 288-299.
    15. Nicholas Ryan, 2017. "The Competitive Effects of Transmission Infrastructure in the Indian Electricity Market," NBER Working Papers 23106, National Bureau of Economic Research, Inc.
    16. Chloé Le Coq & Sebastian Schwenen, 2020. "Financial contracts as coordination device," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(2), pages 241-259, April.
    17. Ali Hortacsu & Jakub Kastl, 2008. "Testing for Common Values in Canadian Treasury Bill Auctions," Discussion Papers 07-053, Stanford Institute for Economic Policy Research.
    18. Jason Allen & Jakub Kastl & Milena Wittwer, 2020. "Primary Dealers and the Demand for Government Debt," Staff Working Papers 20-29, Bank of Canada.
    19. Hunt Allcott, 2012. "The Smart Grid, Entry, and Imperfect Competition in Electricity Markets," NBER Working Papers 18071, National Bureau of Economic Research, Inc.
    20. Milena Wittwer, 2021. "Connecting Disconnected Financial Markets?," American Economic Journal: Microeconomics, American Economic Association, vol. 13(1), pages 252-282, February.
    21. Kastl, Jakub, 2020. "Auctions in financial markets," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    22. Pietro Bonaldi & Ali Hortacsu & Zhaogang Song, 2015. "An Empirical Test of Auction Efficiency: Evidence from MBS Auctions of the Federal Reserve," Finance and Economics Discussion Series 2015-82, Board of Governors of the Federal Reserve System (U.S.).
    23. 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.
    24. Wittwer, Milena, 2020. "Interconnected pay-as-bid auctions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 506-530.

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