TY - GEN

T1 - The price of stochastic anarchy

AU - Chung, Christine

AU - Ligett, Katrina

AU - Pruhs, Kirk

AU - Roth, Aaron

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=44449083842&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-79309-0_27

DO - 10.1007/978-3-540-79309-0_27

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AN - SCOPUS:44449083842

SN - 3540793089

SN - 9783540793083

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 303

EP - 314

BT - Algorithmic Game Theory - First International Symposium, SAGT 2008, Proceedings

T2 - 1st International Symposium on Algorithmic Game Theory, SAGT 2008

Y2 - 30 April 2008 through 2 May 2008

ER -