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Auction design with ambiguity: Optimality of the first-price auction

Author

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  • Hwang, Sung-Ha
  • Koh, Youngwoo
  • Baik, Sosung

Abstract

We study the optimal auction design problem when bidders are ambiguity averse and follow the max-min expected utility model. Each bidder’s set of priors consists of beliefs that are close to the seller’s belief, where “closeness” is defined by a divergence. For a given allocation rule, we show that optimal transfers belong to a specific class of transfers, termed win-lose dependent transfers, in which bidders’ transfers upon winning and losing depend only on their own types but not on their opponents’ type reports. This result effectively reduces the infinite-dimensional problem of identifying an optimal transfer function into a two-dimensional problem of determining two constants-one for winning and another for losing. Solving this reduced problem, we show that among efficient mechanisms without transfers to losing bidders, the first-price auction is optimal, thereby outperforming other auction formats such as the second-price auction. We also discuss how the structure of the set of priors is related to the revenue ranking between the first- and second-price auctions.

Suggested Citation

  • Hwang, Sung-Ha & Koh, Youngwoo & Baik, Sosung, 2026. "Auction design with ambiguity: Optimality of the first-price auction," Games and Economic Behavior, Elsevier, vol. 157(C), pages 298-321.
    • Handle: RePEc:eee:gamebe:v:157:y:2026:i:c:p:298-321
    DOI: 10.1016/j.geb.2026.02.001
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    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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