Regret minimization and the price of total anarchy

Avrim Blum*, Mohammad Taghi Hajiaghayi, Aaron Roth, Katrina Ligett

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

88 Scopus citations


We propose weakening the assumption made when studying the price of anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total anarchy" matches the Nash price of anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of anarchy and the recently introduced price of sinking [15], which require all players to behave in a prescribed manner, we show that the price of total anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total anarchy is an upper bound on the price of anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of anarchy in mixed strategies.

Original languageAmerican English
Title of host publicationSTOC'08
Subtitle of host publicationProceedings of the 2008 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Print)9781605580470
StatePublished - 2008
Externally publishedYes
Event40th Annual ACM Symposium on Theory of Computing, STOC 2008 - Victoria, BC, Canada
Duration: 17 May 200820 May 2008

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference40th Annual ACM Symposium on Theory of Computing, STOC 2008
CityVictoria, BC


  • Algorithmic game theory
  • Nash equilibria
  • Regret minimization

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