The price of stochastic anarchy

Christine Chung*, Katrina Ligett, Kirk Pruhs, Aaron Roth

*Corresponding author for this work

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

15 Scopus citations


We consider the solution concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of (Nash) anarchy for quantifying the cost of selfishness and lack of coordination in games. As a solution concept, the Nash equilibrium has disadvantages that the set of stochastically stable states of a game avoid: unlike Nash equilibria, stochastically stable states are the result of natural dynamics of computationally bounded and decentralized agents, and are resilient to small perturbations from ideal play. The price of stochastic anarchy can be viewed as a smoothed analysis of the price of anarchy, distinguishing equilibria that are resilient to noise from those that are not. To illustrate the utility of stochastic stability, we study the load balancing game on unrelated machines. This game has an unboundedly large price of Nash anarchy even when restricted to two players and two machines. We show that in the two player case, the price of stochastic anarchy is 2, and that even in the general case, the price of stochastic anarchy is bounded. We conjecture that the price of stochastic anarchy is O(m), matching the price of strong Nash anarchy without requiring player coordination. We expect that stochastic stability will be useful in understanding the relative stability of Nash equilibria in other games where the worst equilibria seem to be inherently brittle.

Original languageAmerican English
Title of host publicationAlgorithmic Game Theory - First International Symposium, SAGT 2008, Proceedings
Number of pages12
StatePublished - 2008
Externally publishedYes
Event1st International Symposium on Algorithmic Game Theory, SAGT 2008 - Paderborn, Germany
Duration: 30 Apr 20082 May 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4997 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference1st International Symposium on Algorithmic Game Theory, SAGT 2008


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