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Substitute goods, auctions, and equilibrium

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  • Milgrom, Paul
  • Strulovici, Bruno

Abstract

This paper identifies two notions of substitutes for auction and equilibrium analysis. Weak substitutes, the usual price-theory notion, guarantees monotonicity of Tatonnement processes and convergence of clock auctions to a pseudo-equilibrium, but only strong substitutes, which treats each unit traded as a distinct good with its own price, guarantees that every pseudo-equilibrium is a Walrasian equilibrium, that the Vickrey outcome is in the core, and that the "law of aggregate demand" is satisfied. When goods are divisible, weak substitutes along with concavity guarantees all of the above properties, except for the law of aggregate demand.

Suggested Citation

  • Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
    • Handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:212-247
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    References listed on IDEAS

    as
    1. 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.
    2. Milgrom, Paul, 1994. "Comparing Optima: Do Simplifying Assumptions Affect Conclusions?," Journal of Political Economy, University of Chicago Press, vol. 102(3), pages 607-615, June.
    3. 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.
    4. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    5. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    6. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    7. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    8. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
    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.
    10. 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.
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