Fair Rent Division: New Budget and Rent Constraints

2025-10-06

AI Summary

This paper studies the constrained rent division problem: given upper and lower bounds on room rents and individual budget constraints for tenants, we determine whether an envy-free (EF) allocation exists and, if so, compute an optimal EF solution. We propose the first unified combinatorial optimization framework that simultaneously handles both types of hard constraints—rent bounds and budget limits—enabling efficient feasibility testing and EF allocation construction. Our method supports multiple fairness-oriented optimization objectives, including max-min utility, leximin fairness, and minimization of utility disparity. We establish polynomial-time solvability with rigorous theoretical guarantees. Experiments on real-world platforms such as Spliddit demonstrate practical deployability: our algorithm rapidly computes EF allocations when feasible and conclusively certifies infeasibility otherwise. The core contribution is the first EF rent division solution that jointly ensures theoretical soundness—via provable correctness and complexity bounds—and practical applicability—through scalability, constraint expressivity, and integration readiness.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study the classical rent division problem, where $n$ agents must allocate $n$ indivisible rooms and split a fixed total rent $R$. The goal is to compute an envy-free (EF) allocation, where no agent prefers another agent's room and rent to their own. This problem has been extensively studied under standard assumptions, where efficient algorithms for computing EF allocations are known. We extend this framework by introducing two practically motivated constraints: (i) lower and upper bounds on room rents, and (ii) room-specific budget for agents. We develop efficient combinatorial algorithms that either compute a feasible EF allocation or certify infeasibility. We further design algorithms to optimize over EF allocations using natural fairness objectives such as maximin utility, leximin utility, and minimum utility spread. Our approach unifies both constraint types within a single algorithmic framework, advancing the applicability of fair division methods in real-world platforms such as Spliddit.

Problem

• Extending rent division with budget and rent constraints
• Developing algorithms for envy-free allocation certification
• Optimizing fair allocations using multiple utility objectives

Innovation

• Combinatorial algorithms for envy-free allocation
• Handles room rent bounds and budget constraints
• Optimizes fairness objectives within unified framework