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Optimal Selling Mechanisms under Imperfect Commitment: Extending to the Multi-Period Case

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  • Juan I. Beccuti

Abstract

This paper studies the optimal mechanism for a seller (she) that sells, in a sequence of periods, an indivisible object per period to the same buyer (he). Buyer's willingness to pay remains constant along time and is his private information. The seller can commit to the current period mechanism but not to future ones. Our main result is that a seller cannot do better than posting a price in every period. We give a complete characterization of the optimal mechanism and equilibrium payoffs for every prior. Also, we show that, when agents are arbitrarily patient, the seller does not learn about buyer's type except in extreme cases, posting a price equal to the minimum buyer's willingness to pay in every period. This result is a reminiscence of the Coase's conjecture, where a monopolist cannot exert her monopoly power due to the lack of long-term commitment.

Suggested Citation

  • Juan I. Beccuti, 2014. "Optimal Selling Mechanisms under Imperfect Commitment: Extending to the Multi-Period Case," Diskussionsschriften dp1402, Universitaet Bern, Departement Volkswirtschaft.
    • Handle: RePEc:ube:dpvwib:dp1402
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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. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, April.
    3. Bester, Helmut & Strausz, Roland, 2000. "Imperfect commitment and the revelation principle: the multi-agent case," Economics Letters, Elsevier, vol. 69(2), pages 165-171, November.
    4. Helmut Bester & Roland Strausz, "undated". "Imperfect Commitment and the Revelation Principle," Papers 004, Departmental Working Papers.
    5. Schmidt Klaus M., 1993. "Commitment through Incomplete Information in a Simple Repeated Bargaining Game," Journal of Economic Theory, Elsevier, vol. 60(1), pages 114-139, June.
    6. 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.
    7. Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-149, April.
    8. Vasiliki Skreta, 2005. "Extensions on "Sequentially Optimal Mechanisms"," UCLA Economics Online Papers 343, UCLA Department of Economics.
    9. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    10. Juan I. Beccuti, 2014. "Optimal Selling Mechanisms under Imperfect Commitment," Diskussionsschriften dp1401, Universitaet Bern, Departement Volkswirtschaft.
    11. Vasiliki Skreta, 2006. "Sequentially Optimal Mechanisms -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1085-1111.
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    Cited by:

    1. Juan I. Beccuti, 2014. "Optimal Selling Mechanisms under Imperfect Commitment," Diskussionsschriften dp1401, Universitaet Bern, Departement Volkswirtschaft.

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    More about this item

    Keywords

    asymmetric information; dynamics; optimal mechanism; imperfect commitment;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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