Fair Coordination in Strategic Scheduling
Wei-Chen Lee, Martin Bullinger, Alessandro Abate, Michael Wooldridge
TL;DR
<3-5 sentence high-level summary>We study a strategic variant of the identical-machine scheduling problem where jobs (players) have weights and choose among identical machines. The paper introduces a hierarchy of fairness concepts (credibility, equality, envy-based notions, and monotonicity) and a unified Sequential Contiguous Assignment (SCA) framework that achieves these properties by tailoring its subroutines. A complete complexity landscape is provided, showing many combinations are solvable in polynomial time while others are NP-hard, with contiguity playing a central role in tractability. The results illuminate how enforcing natural fairness constraints can render otherwise intractable scheduling problems solvable and suggest avenues for price-of-fairness analysis and fair partitioning in distributed systems.
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.