Costly auction entry, royalty payments, and the optimality of asymmetric designs

Dan Bernhardt, Tingjun Liu, Takeharu Sogo

Research output: Contribution to journalArticlepeer-review


We analyze optimal auction mechanisms when bidders base costly entry decisions on their valuations, and bidders pay with a fixed royalty rate plus cash. With sufficient valuation uncertainty relative to entry costs, the optimal mechanism features asymmetry so that bidders enter with strictly positive but different (ex-ante) probabilities. When bidders are ex-ante identical, higher royalty rates—which tie payments more closely to bidder valuations—increase the optimal degree of asymmetry in auction design, further raising revenues. When bidders differ ex-ante in entry costs, the seller favors the low cost entrant; whereas when bidders have different valuation distributions, the seller favors the weaker bidder if entry costs are low, but not if they are high. Higher royalty rates cause the seller to favor the weaker bidder by less, and the strong bidder by more.

Original languageEnglish (US)
Article number105041
JournalJournal of Economic Theory
StatePublished - Jul 2020


  • Asymmetric auctions
  • Auctions with participation costs
  • Heterogeneous bidders
  • Optimal auctions
  • Royalty payments

ASJC Scopus subject areas

  • Economics and Econometrics


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