Journal of the ACM (JACM)
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Fast convergence to Wardrop equilibria by adaptive sampling methods
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Tradeoffs in worst-case equilibria
Theoretical Computer Science - Approximation and online algorithms
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Game Theory
The complexity of game dynamics: BGP oscillations, sink equilibria, and beyond
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Regret minimization and the price of total anarchy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Strong price of anarchy for machine load balancing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
The Price of Malice in Linear Congestion Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Stochastic Stability in Internet Router Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On the Inefficiency Ratio of Stable Equilibria in Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Tradeoffs and Average-Case Equilibria in Selfish Routing
ACM Transactions on Computation Theory (TOCT)
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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We consider the solution concept of stochastic stability, and propose the price of stochastic anarchyas an alternative to the price of (Nash) anarchyfor 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.