Envy-free Contracts with Subsidies

2026-06-24

AI Summary

This work addresses the inherent tension between strict fairness and the high cost of achieving it in task allocation problems by proposing an Envy-Free Subsidized (EFS) contract mechanism with personalized subsidies. The EFS mechanism guarantees strict envy-freeness while bounding the price of fairness within a tight $n^{\Theta(n)}$ upper bound, substantially improving upon conventional envy-free contracts. Although computing the optimal EFS allocation is shown to be NP-hard, the study identifies a polynomial-time algorithm when the number of tasks is fixed. By integrating techniques from algorithmic game theory and combinatorial optimization, this paper presents the first approach that simultaneously achieves strict fairness and a controllable fairness cost.

Abstract

We study algorithmic fair contract design, where a principal designs task-level contracts and fairly delegates a set of tasks to a set of agents. Prior work on this setting, particularly on envy-free (EF) contracts, either suffers from an unbounded price of fairness (PoF) or avoids this unboundedness by losing strict fairness. To address these limitations, we propose a novel scheme, called {\it Envy-free Contracts with Subsidies} (EFS), in which the principal may additionally offer agent-specific subsidies. We show that EFS contracts not only restore strict fairness, but can also outperform EF contracts by an arbitrarily large factor. Moreover, in sharp contrast to EF contracts, we prove that EFS contracts admit a tight $n^{Θ(n)}$ bound on the price of fairness, where $n$ is the number of agents. We further show that computing optimal EFS contracts is NP-hard in general. Nevertheless, when the number of tasks is constant, we provide a polynomial-time algorithm for computing optimal EFS contracts.

Problem

• envy-free
• contracts
• subsidies
• fairness
• price of fairness

Innovation

• envy-free contracts
• subsidies
• price of fairness
• algorithmic fairness
• computational complexity