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A Characterization of the Conditions for Optimal Auction with Resale

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  • Mylovanov, Tymofiy
  • Tröger, Thomas

Abstract

Zheng has proposed a seller-optimal auction for (asymmetric) independent-privatevalue environments where inter-bidder resale is possible. Zheng’s construction requires novel conditions — Resale Monotonicity, Transitivity, and Invariance — on the bidders’ value distribution profile. The only known examples of distribution profiles satisfying these conditions in environments with three or more bidders are uniform distributions. Our characterization result shows that Zheng’s conditions, while being strong, are satisfied by many non-uniform distribution profiles. A crucial step in our analysis is to show that Invariance implies Resale Monotonicity and Transitivity.

Suggested Citation

  • Mylovanov, Tymofiy & Tröger, Thomas, 2006. "A Characterization of the Conditions for Optimal Auction with Resale," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 128, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  • Handle: RePEc:trf:wpaper:128
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    File URL: https://epub.ub.uni-muenchen.de/13423/1/128.pdf
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    References listed on IDEAS

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    1. Vasiliki Skreta, 2000. "Sequentially Optimal Mechanisms," Econometric Society World Congress 2000 Contributed Papers 1521, Econometric Society.
    2. Tymofiy Mylovanov & Thomas Tröger, 2005. "A note on Zheng’s conditions for implementing an optimal auction with resale," Bonn Econ Discussion Papers bgse29_2005, University of Bonn, Germany.
    3. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Bester, Helmut & Strausz, Roland, 2001. "Contracting with Imperfect Commitment and the Revelation Principle: The Single Agent Case," Econometrica, Econometric Society, vol. 69(4), pages 1077-1098, July.
    5. Giacomo Calzolari & Alessandro Pavan, 2006. "Monopoly with resale," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 362-375, June.
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    Cited by:

    1. Gábor Virág, 2013. "First-price auctions with resale: the case of many bidders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 129-163, January.
    2. Rodney J. Garratt & Thomas Trˆger & Charles Z. Zheng, 2009. "Collusion via Resale," Econometrica, Econometric Society, vol. 77(4), pages 1095-1136, July.

    More about this item

    Keywords

    independent private values; optimal auction; resale; inverse virtual valuation function;

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