Correlated and Coarse Equilibria of Single-Item Auctions

  • Michal Feldman
  • Brendan LucierEmail author
  • Noam Nisan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10123)


We study correlated equilibria and coarse equilibria of simple first-price single-item auctions in the simplest auction model of full information. Nash equilibria are known to always yield full efficiency and a revenue that is at least the second-highest value. We prove that the same is true for all correlated equilibria, even those in which agents overbid – i.e., bid above their values.

Coarse equilibria, in contrast, may yield lower efficiency and revenue. We show that the revenue can be as low as \(26\%\) of the second-highest value in a coarse equilibrium, even if agents are assumed not to overbid, and this is tight. We also show that when players do not overbid, the worst-case bound on social welfare at coarse equilibrium improves from \(63\%\) of the highest value to \(81\%\), and this bound is tight as well.


Nash Equilibrium Price Auction Correlate Equilibrium Pure Nash Equilibrium Bayesian Setting 
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Copyright information

© Springer-Verlag GmbH Germany 2016

Authors and Affiliations

  1. 1.Tel Aviv UniversityTel AvivIsrael
  2. 2.Microsoft ResearchRedmondUSA
  3. 3.Hebrew UniversityJerusalemIsrael

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