Price of Anarchy for Maximizing the Minimum Machine Load

Abstract

The maximizing the minimum machine delay game (or cover game) with uniformly
related machines is considered. Players choose machines with different speeds to run their jobs
trying to minimize job’s delay, i.e. the chosen machine’s completion time. The social payoff is
the minimal delay over all machines. For the general case of N machines we found the lower
bound for Price of Anarchy (PoA), and for the case of 3 machines we found its exact value. We
proved that the PoA does not change or increases when an additional third machine is included
into the system with two machines. Also we propose a method of computation the PoA value and
illustrate it for 3 machines.