Fair Coordination in Strategic Scheduling

2025-12-15

AI Summary

This paper investigates fair scheduling of multi-weighted strategic jobs on identical machines, jointly ensuring game-theoretic stability (Nash equilibrium) and fairness—namely, load equality among equally weighted jobs, weighted envy-freeness, and its natural relaxations. We first establish a hierarchical framework for weighted fairness and introduce *weight-aware relaxed envy-freeness*. Systematically analyzing the joint satisfiability of fairness properties—individually and in combination—with Nash equilibrium, we derive a complete computational complexity landscape. Crucially, under makespan minimization, we prove that several key fairness constraints admit polynomial-time algorithms. Our primary contribution is a unified model integrating fairness and strategic robustness, bridging fair allocation theory and strategic scheduling through combinatorial game-theoretic analysis and constrained optimization.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

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.

Problem

• Strategic scheduling with fairness and credibility constraints
• Complexity analysis of envy-freeness and equality properties
• Algorithmic approach for makespan optimization under fairness

Innovation

• Strategic scheduling with fairness and Nash equilibrium
• Hierarchy of envy-freeness properties for job weights
• Unified algorithmic approach with fine-tuned subroutines