We investigate the price of anarchy of a load balancing 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 processor-sharing 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. Independent of the state of the servers, each dispatcher
seeks to determine the routing strategy that optimizes the performance for its own traffic. The …

We investigate the price of anarchy of a load balancing 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 processor-sharing 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 worst-case Nash equilibrium occurs when each player routes exactly the …