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Substitute Valuations, Auctions, and Equilibrium with Discrete Goods

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Author Info
Paul Milgrom
Bruno Stulovici

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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: 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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Find related papers by JEL classification:
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium

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  1. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May. [Downloadable!] (restricted)
  2. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September. [Downloadable!] (restricted)
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  3. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July. [Downloadable!] (restricted)
  4. 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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  5. Lawrence Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 1(1), pages 1019-1019. [Downloadable!] (restricted)
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  6. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November. [Downloadable!] (restricted)
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