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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.

Suggested Citation

  • Bruno Strulovici & Paul Milgrom, 2007. "Substitute Valuations, Auctions, and Equilibrium with Discrete Goods," Economics Series Working Papers 339, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:339
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    References listed on IDEAS

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    1. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    2. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    3. 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.
    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.
    5. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    6. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    7. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
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    More about this item

    Keywords

    Substitute Valuation; Auction; Discrete Goods; Nonlinear Price; Submodular Dual; Walrasian Equilibrium; Pseudo-Equilibrium; Law of Aggregate Demand; Vickrey Auction;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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