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A Double-Track Auction for Substitutes and Complements

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Author Info
Ning Sun () (School of Economics, Shanghai University of Finance and Economics)
Zaifu Yang () (Faculty of Business Administration, Yokohama National University)
Abstract

We propose a new t^atonnement process called a double-track auction for eciently allocating multiple heterogeneous indivisible items in two distinct sets S1 and S2 to many buyers who view items in the same set as substitutes but items across the two sets as complements. The auctioneer initially announces suciently low prices for items in one set, say S1, but suciently high prices for items in the other set S2. In each round, the buyers respond by reporting their demands at the current prices and the auctioneer adjusts prices upwards for items in S1 but downwards for items in S2 based on buyers' reported demands until the market is clear. Unlike any existing auction, this auction is a blend of a multi-item ascending auction and a multi-item descending auction. We prove that the auction nds an ecient allocation and its market-clearing prices in nitely many rounds. Based on the auction we also establish a dynamic, ecient and strategy-proof mechanism.

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Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 656.

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Length: 34pages
Date of creation: Jul 2008
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Handle: RePEc:kyo:wpaper:656

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Related research
Keywords: Market design; dynamic auction; t^atonnement process; gross substitutes and complements; Walrasian equilibrium; incentives.;

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  2. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Papers 2004-W09, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. [Downloadable!] (restricted)
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  6. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn. [Downloadable!] (restricted)
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  9. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June. [Downloadable!] (restricted)
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  12. Bevia, Carmen & Quinzii, Martine & Silva, Jose A., 1999. "Buying several indivisible goods," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 1-23, January. [Downloadable!] (restricted)
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  13. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July. [Downloadable!] (restricted)
  14. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April. [Downloadable!] (restricted)
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  15. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March. [Downloadable!] (restricted)
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  24. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March. [Downloadable!] (restricted)
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