Price of anarchy in machine load balancing game

This paper considers the machine load balancing game with uniformly related machines. Players choose machines of different speeds to run their jobs striving to minimize job’s delay, i.e., the job completion time on a chosen machine. The social cost is the maximum delay over all machines. In the general case and the special case of 3 machines, we obtain upper estimates for the price of anarchy (PoA) and demonstrate when they coincide with the exact values. Moreover, sufficient conditions for PoA increase are established under new machine inclusion into the system. And finally, we propose a computing algorithm of the exact PoA value in the three-machine model.