Robust auction design under multiple priors by linear and integer programming

Abstract

It is commonly assumed in the optimal auction design literature that valuations of buyers are independently drawn from a unique distribution. In this paper we study auctions under ambiguity, that is, in an environment where valuation distribution is uncertain itself, and present a linear programming approach to robust auction design problem with a discrete type space. We develop an algorithm that gives the optimal solution to the problem under certain assumptions when the seller is ambiguity averse with a finite prior set \({\mathcal {P}}\) and the buyers are ambiguity neutral with a prior \(f\in {\mathcal {P}}\). We also consider the case where all parties, the buyers and the seller, are ambiguity averse, and formulate this problem as a mixed integer programming problem. Then, we propose a hybrid algorithm that enables to compute an optimal solution for the problem in reduced time.

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Fig. 1

Notes

  1. 1.

    A full insurance mechanism is one where the ex-post pay-off of a given type of bidder does not vary with the report of a competing bidder.

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Correspondence to Mustafa Ç. Pınar.

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Koçyiğit, Ç., Bayrak, H.I. & Pınar, M.Ç. Robust auction design under multiple priors by linear and integer programming. Ann Oper Res 260, 233–253 (2018). https://doi.org/10.1007/s10479-017-2416-4

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Keywords

  • Optimal auction design
  • Robustness
  • Multiple priors
  • Ambiguity
  • Linear programming
  • Mixed-integer programming