On Revenue-Maximizing Mechanisms Assuming Convex Costs

  • Amy Greenwald
  • Takehiro OyakawaEmail author
  • Vasilis Syrgkanis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11059)


We investigate revenue-maximizing mechanisms in settings where bidders’ utility functions are characterized by convex costs. Such costs arise, for instance, in procurement auctions for energy, and when bidders borrow money at non-linear interest rates. We provide a 1 / 16e approximation guarantee for a prior-free randomized mechanism when bidders’ values are drawn from MHR distributions, and their costs are polynomial. Additionally, we propose two heuristics that allocate proportionally, using either bidders’ values or virtual values. Perhaps surprisingly, in the convex cost setting, it is preferable to allocate to multiple relatively high bidders, rather than only to bidders with the highest (virtual) value, as is optimal in the traditional quasi-linear utility setting.


Mechanism design Optimal auction Prior-free 



This research was supported by NSF Grant #1217761 and Microsoft Research.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Amy Greenwald
    • 1
  • Takehiro Oyakawa
    • 1
    Email author
  • Vasilis Syrgkanis
    • 2
  1. 1.Brown UniversityProvidenceUSA
  2. 2.Microsoft ResearchCambridgeUSA

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