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Substitute Valuations, Auctions, and Equilibrium with Discrete Goods

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  • Bruno Strulovici
  • Paul Milgrom

Abstract

For economies in which goods are available in several (discrete) units, this paper identifies two notions of substitutes. The weaker notion guarantees monotonicity of tatonnement processses and convergence of clock auctions to a pseudo-equilibrium, but only the stronger notion, which treats each unit traded as a distinct good with its own price, guarantees that every pseudo-equilibrium is a Walrasian equilibrium, the Vickrey outcome is in the core, and the law of aggregate demand is satisfied. The paper provides several characterizations and properties of weak and strong substitutes.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 339.

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Date of creation: 01 Aug 2007
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Handle: RePEc:oxf:wpaper:339

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Keywords: Substitute Valuation; Auction; Discrete Goods; Nonlinear Price; Submodular Dual; Walrasian Equilibrium; Pseudo-Equilibrium; Law of Aggregate Demand; Vickrey Auction;

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  1. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, American Economic Association, vol. 95(4), pages 913-935, September.
  2. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 108(2), pages 245-272, April.
  3. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
  4. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers, Stanford University, Department of Economics 02004, Stanford University, Department of Economics.
  5. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, Elsevier, vol. 87(1), pages 95-124, July.
  6. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, Elsevier, vol. 92(1), pages 66-95, May.
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