TY - GEN

T1 - Routing without regret

T2 - 25th Annual ACM Symposium on Principles of Distributed Computing 2006

AU - Blum, Avrim

AU - Even-Dar, Eyal

AU - Ligett, Katrina

PY - 2006

Y1 - 2006

N2 - There has been substantial work developing simple, efficient no-regret algorithms for a wide class of repeated decision-making problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversarially-changhig environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question; if each player in a routing game uses a no-regret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games have substantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimal agents, behavior will approach Nash, equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that depends polynomially on the players' regret bounds and the maximum slope of any latency function. We also show that price-of-anarchy results may be applied to these approximate equilibria, and also consider the finite-size (non-infinitesimal) load-balancing model of Azar [2].

AB - There has been substantial work developing simple, efficient no-regret algorithms for a wide class of repeated decision-making problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversarially-changhig environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question; if each player in a routing game uses a no-regret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games have substantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimal agents, behavior will approach Nash, equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that depends polynomially on the players' regret bounds and the maximum slope of any latency function. We also show that price-of-anarchy results may be applied to these approximate equilibria, and also consider the finite-size (non-infinitesimal) load-balancing model of Azar [2].

KW - Game theory

KW - Network games

UR - http://www.scopus.com/inward/record.url?scp=33748692398&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33748692398

SN - 1595933840

SN - 9781595933843

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 45

EP - 52

BT - Proceedings of the 25th Annual ACM Symposium on Principles of Distributed Computing 2006

Y2 - 23 July 2006 through 26 July 2006

ER -