Fair Contracts

2025-07-15

AI Summary

This paper studies optimal contract design under fairness constraints, introducing envy-freeness (EF) and its relaxations—ε-envy-freeness (ε-EF) and envy-freeness up to one task (EF1)—into contract theory for the first time. It models fairness in task allocation and compensation, proving the existence of EF contracts. When either the number of agents or tasks is constant, it provides polynomial-time algorithms for computing optimal EF contracts and a fully polynomial-time approximation scheme (FPTAS) for ε-EF contracts. It further establishes the first tight characterization of the fairness cost of EF1 contracts, yielding a Ω(√n)–O(n²) bound. The core contribution lies in establishing a formal theoretical connection between fairness and contract design, moving beyond the traditional efficiency-first paradigm. This work introduces a novel framework for jointly optimizing fairness and incentive compatibility in mechanism design, accompanied by computationally tractable tools.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

We introduce and study the problem of designing optimal contracts under fairness constraints on the task assignments and compensations. We adopt the notion of envy-free (EF) and its relaxations, $ε$-EF and envy-free up to one item (EF1), in contract design settings. Unlike fair allocations, EF contracts are guaranteed to exist. However, computing any constant-factor approximation to the optimal EF contract is NP-hard in general, even using $ε$-EF contracts. For this reason, we consider settings in which the number of agents or tasks is constant. Notably, while even with three agents, finding an EF contract better than $2/5$ approximation of the optimal is NP-hard, we are able to design an FPTAS when the number of agents is constant, under relaxed notions of $ε$-EF and EF1. Moreover, we present a polynomial-time algorithm for computing the optimal EF contract when the number of tasks is constant. Finally, we analyze the price of fairness in contract design. We show that the price of fairness for exact EF contracts can be unbounded, even with a single task and two agents. In contrast, for EF1 contracts, the price of fairness is bounded between $Ω(sqrt{n})$ and $O(n^2)$, where $n$ is the number of agents.

Problem

• Designing optimal contracts with fairness constraints
• Computing EF contract approximations is NP-hard
• Analyzing price of fairness in contract design

Innovation

• Adopts envy-free (EF) in contract design
• Develops FPTAS for constant agent count
• Presents polynomial-time algorithm for constant tasks