Coordinating oligopolistic players in unrelated machine scheduling

We consider the following machine scheduling game. Jobs, controlled by selfish players, are to be assigned to unrelated machines. A player cares only about the finishing time of his job(s), while disregarding the welfare of other players. The outcome of such games is measured by the makespan. Our goal is to design coordination mechanisms to schedule the jobs so as to minimize the price of anarchy. We introduce oligopolistic players. Each such player controls a set of jobs, with the aim of minimizing the sum of the completion times of his jobs. Our model of oligopolistic players is a natural generalization of the conventional model, where each player controls only a single job. In our setting, previous mechanisms designed for players with single jobs are inadequate, e.g., having large price of anarchy, or not guaranteeing pure Nash equilibria. To meet this challenge, we design three mechanisms that are adapted/generalized from Caragiannis’ ACOORD. All our mechanisms induce pure Nash equilibria while guaranteeing relatively small price of anarchy.