Analyzing the price of fairness in scheduling problems with two agents

This paper focuses on the price of fairness in several scheduling problems with two agents, each with a set of nonpreemptive jobs, competing to execute their respective jobs on a single machine. Each agent expects to minimize its objective function, which depends on the completion times of its own jobs. Several objective functions are considered, including makespan, total (weighted) completion time and maximum tardiness. We focus on problems in which both agents pursue the same objective function. For each problem, we analyze the price of fairness and the complexity to find the fairness schedules among the Pareto optimal schedules. When the objective functions of both agents are total completion time, we design an algorithm to generate a near-fair solution and analyze its price of fairness.