Fair Coordination in Strategic Scheduling

TL;DR

This paper explores fair and credible scheduling strategies for strategic agents, balancing Nash equilibrium, fairness, and efficiency, and provides a comprehensive complexity analysis with a unified algorithmic framework.

Contribution

It introduces a complete complexity landscape for fairness and credibility constraints in strategic scheduling and develops a unified algorithmic approach to achieve various fairness properties.

Findings

Complete complexity classifications for fairness and credibility constraints.

A unified algorithmic framework for achieving different fairness properties.

Insights into the trade-offs between fairness, credibility, and makespan optimization.

Abstract

We consider a scheduling problem of strategic agents representing jobs of different weights. Each agent has to decide on one of a finite set of identical machines to get their job processed. In contrast to the common and exclusive focus on makespan minimization, we want the outcome to be fair under strategic considerations of the agents. Two natural properties are credibility, which ensures that the assignment is a Nash equilibrium and equality, requiring that agents with equal-weight jobs are assigned to machines of equal load. We combine these two with a hierarchy of fairness properties based on envy-freeness together with several relaxations based on the idea that envy seems more justified towards agents with a higher weight. We present a complete complexity landscape for satisfiability and decision versions of these properties, alone or in combination, and study them as structural constraints under makespan optimization. For our positive results, we develop a unified algorithmic approach, where we achieve different properties by fine-tuning key subroutines.