 
Summary: Price of Anarchy
in NonCooperative Load Balancing
U. Ayesta1,3, O. Brun2, B.J. Prabhu2
1 BCAM, Basque Center for Applied Mathematics, 48160 Derio, Spain
2 CNRS ; LAAS ; 7 avenue du colonel Roche, 31077 Toulouse, France
3 IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
AbstractWe investigate the price of anarchy of a load balanc
ing game with K dispatchers. 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.
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 amount of traffic, i.e., when
the game is symmetric. For this symmetric game, we provide the
expression for the loads on the servers at the Nash equilibrium.
Using this result we then show that, for a system with two or
more servers, the price of anarchy, which is the worstcase ratio
