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Affliation in Multi-Unit Auctions

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  • Ahmed Anwar

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Abstract

We extend Milgrom and Weber’s affiliated valuations model to the multi-unit case with constant marginal valuations where 2 bidders compete for k identical objects. We show that the discriminatory auction has a unique equilibrium, that corresponds to Milgrom and Weber’s firstprice equilibrium. This unique equilibrium therefore leads to lower expected prices than the equilibrium of the English auction where the units are bundled together. Hence we show that in a common value auction of a single object where the object can be divided into k parts, it is not possible to increase revenue by using a multi-unit discriminatory auction. We discuss a possible application to Treasury auctions.

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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 58.

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Length: 16
Date of creation: Apr 2004
Date of revision:
Handle: RePEc:edn:esedps:58

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Keywords: Affiliated Valuations; Multi-Unit Auctions; Treasury Auctions.;

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  1. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  2. Kjell G. Nyborg & Kristian Rydqvist & Suresh M. Sundaresan, 2002. "Bidder Behavior in Multiunit Auctions: Evidence from Swedish Treasury Auctions," Journal of Political Economy, University of Chicago Press, vol. 110(2), pages 394-424, April.
  3. 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.
  4. Engelbrecht-Wiggans, Richard & Kahn, Charles M., 1998. "Multi-Unit Pay-Your-Bid Auctions with Variable Awards," Games and Economic Behavior, Elsevier, vol. 23(1), pages 25-42, April.
  5. Wilson, Robert, 1979. "Auctions of Shares," The Quarterly Journal of Economics, MIT Press, vol. 93(4), pages 675-89, November.
  6. 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.
  7. S. Viswanathan & James J.D. Wang, 2004. "Optimal Bidding in Multi-Unit Discriminatory Auctions: Two Bidders," Econometric Society 2004 North American Winter Meetings 58, Econometric Society.
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