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Optimal selling mechanisms under moment conditions

Author

Listed:
  • Carrasco, Vinicius
  • Farinha Luz, Vitor
  • Kos, Nenad
  • Messner, Matthias
  • Monteiro, Paulo
  • Moreira, Humberto

Abstract

We study the revenue maximization problem of a seller who is partially informed about the distribution of buyer's valuations, only knowing its first N moments. The seller chooses the mechanism generating the best revenue guarantee based on the information available, that is, the optimal mechanism is chosen according to maxmin expected revenue. We show that the transfer function in the optimal mechanism is given by non-negative monotonic hull of a polynomial of degree N. This enables us to transform the seller's problem into a much simpler optimization problem over N variables. The optimal mechanism is found by choosing the coefficients of the polynomial subject to a resource constraint. We show that knowledge of the first moment does not guarantee strictly positive revenue for the seller, characterize the solution for the cases of two moments and derive some characteristics of the solution for the general case.

Suggested Citation

  • Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.
    • Handle: RePEc:eee:jetheo:v:177:y:2018:i:c:p:245-279
    DOI: 10.1016/j.jet.2018.05.005
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    More about this item

    Keywords

    Optimal mechanism design; Robustness; Incentive compatibility; Individual rationality; Ambiguity aversion; Moment conditions;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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