 
Summary: Price of Anarchy in NonCooperative Load Balancing
Games
U. Ayesta1,3
, O. Brun2,4,
, B.J. Prabhu2,4
1 BCAM Basque Center for Applied Mathematics, 48170 Derio, Spain
2 CNRS ; LAAS ; 7 avenue du colonel Roche, F31077 Toulouse, France
3 IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
4Universit´e de Toulouse ; UPS, INSA, INP, ISAE ; LAAS ; F31077 Toulouse, France
Abstract
We investigate the price of anarchy of a load balancing game with K dispatch
ers. The service rates and holding costs are assumed to depend on the server,
and the service discipline is assumed to be processorsharing at each server.
The performance criterion is taken to be the weighted mean number of jobs
in the system, or equivalently, the weighted mean sojourn time in the system.
Independently of the state of the servers, each dispatcher seeks to determine
the routing strategy that optimizes the performance for its own traffic. The
interaction of the various dispatchers thus gives rise to a noncooperative game.
For this game, we first show that, for a fixed amount of total incoming traffic,
the worstcase Nash equilibrium occurs when each player routes exactly the same
