Improved price of anarchy for machine scheduling games with coordination mechanisms

Abstract

We study several machine scheduling games, each involving n jobs to be processed on m uniformly related machines. Each job, as an agent, selects a machine for processing to minimize his disutility (e.g., the completion time of the agent). We analyze the price of anarchy (PoA) for these scheduling games, where the PoA is defined as maximum ratio of the central objective value of the worst pure Nash equilibrium over the optimal central objective value among all problem instances. We improve several existing results in the literature. First, we give an improved upper bound of the PoA for the scheduling game studied by Hoeksma and Uetz (WAOA’11 proceedings of the 9th international conference on approximation and online algorithms, vol 9. Springer, Berlin, pp 261–273, 2011). Then, we present a better lower bound of the PoA for the scheduling game studied by Lee et al. (Eur J Oper Res 220:305–313, 2012). Finally, we provide improved upper bounds of the PoA in terms of the number of machines, for another scheduling game proposed by Chen and Gurel (J Sched 15:157–164, 2012).