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The multiple unit auction with variable supply

  • Yvan Lengwiler

The theory of multiple unit auctions traditionally assumes that the offered quantity is fixed. I argue that this assumption is not appropriate for many applications because the seller may be able and willing to adjust the supply to the bidding. In this paper I address this shortcoming by analyzing a multi-unit auction game between a monopolistic seller who can produce arbitrary quantities at constant unit cost, and oligopolistic bidders. I establish the existence of a subgame-perfect equilibrium for price discriminating and for uniform price auctions. I also show that bidders have an incentive to misreport their true demand in both auction formats, but they do that in different ways and for different reasons. Furthermore, both auction formats are inefficient, but there is no unambiguous ordering among them. Finally, the more competitive the bidders are, the more likely the seller is to prefer uniform pricing over price discrimination, yet increased competition among bidders may or may not enhance efficiency.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 1998-28.

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Date of creation: 1998
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Handle: RePEc:fip:fedgfe:1998-28
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  1. Menezes, Flavio M. & Monteiro, Paulo K., 1995. "Existence of equilibrium in a discriminatory price auction," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 285-292, December.
  2. Lawrence M. Ausubel & Peter Cramton & Marek Pycia & Marzena Rostek & Marek Weretka, 2014. "Demand Reduction and Inefficiency in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1366-1400.
  3. 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.
  4. Robert G. Hansen, 1988. "Auctions with Endogenous Quantity," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 44-58, Spring.
  5. V.V. Chari & Robert J. Weber, 1992. "How the U.S. Treasury should auction its debt," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 3-12.
  6. Ian Gale, 1994. "Competition for scarce inputs: the case of airport takeoff and landing slots," Economic Review, Federal Reserve Bank of Cleveland, issue Q II, pages 18-25.
  7. Nautz, D., 1995. "Optimal bidding in multi-unit auctions with many bidders," Economics Letters, Elsevier, vol. 48(3-4), pages 301-306, June.
  8. Nautz, D. & Wolfstetter, E., 1997. "Bid shading and risk aversion in multi-unit auctions with many bidders," Economics Letters, Elsevier, vol. 56(2), pages 195-200, October.
  9. Hans Haller & Yvan Lengwiler, 1998. "A discrete model of discriminatory price auctions - an alternative to Menezes-Monteiro," Finance and Economics Discussion Series 1998-08, Board of Governors of the Federal Reserve System (U.S.).
  10. Tenorio, Rafael, 1997. "On Strategic Quantity Bidding in Multiple Unit Auctions," Journal of Industrial Economics, Wiley Blackwell, vol. 45(2), pages 207-17, June.
  11. Noussair, Charles, 1995. "Equilibria in a Multi-object Uniform Price Sealed Bid Auction with Multi-unit Demands," Economic Theory, Springer, vol. 5(2), pages 337-51, March.
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