Price of Anarchy in uniform parallel machines scheduling game with weighted completion time as social goal

Abstract

This article investigates the efficiency of Nash equilibria in a utilitarian scheduling game, where each job, acting as an agent, strategically selects a machine for its processing. The study focuses on a uniform parallel machine environment, employing the Weighted Shortest Processing Time rule as the local policy and the total weighted completion time as the social goal. We establish upper and lower bounds for the Price of Anarchy, offering valuable insights for this scheduling game.