When is Truthfully Allocating Chores no Harder than Goods?

2025-05-02

AI Summary

This paper studies fair, efficient, and incentive-compatible allocation of chores (items yielding negative utility) among strategic agents. For both indivisible and divisible chores, we introduce a bundle-exchange transformation technique, establishing the first systematic mapping between truthful mechanisms for goods and chores. We fully characterize the structure of truthful mechanisms in the two-agent setting and prove that their efficiency ratio is identically zero. We construct the first deterministic, truthful, envy-free, and proportional mechanism for divisible chores under arbitrary numbers of agents. For indivisible chores with bi-valued costs, we design a randomized mechanism achieving ex-ante Pareto optimality, ex-ante envy-freeness, and ex-post envy-freeness up to one chore (EF1). These results fill critical gaps in the mechanism design theory of chore allocation, advancing foundational understanding of fairness and incentives in negative-utility settings.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division
• Reasoning under Uncertainty: Decision/Utility Theory

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 problem of fairly and efficiently allocating a set of items among strategic agents with additive valuations, where items are either all indivisible or all divisible. When items are emph{goods}, numerous positive and negative results are known regarding the fairness and efficiency guarantees achievable by emph{truthful} mechanisms, whereas our understanding of truthful mechanisms for emph{chores} remains considerably more limited. In this paper, we discover various connections between truthful good and chore allocations, greatly enhancing our understanding of the latter via tools from the former. For indivisible chores with two agents, we observe that a simple bundle-swapping operation transforms several properties for goods including truthfulness to the corresponding properties for chores, which enables us to characterize truthful mechanisms and derive the tight guarantees of various fairness notions achieved by truthful mechanisms. Moreover, for divisible chores, by generalizing the above transformation to an arbitrary number of agents, we characterize truthful mechanisms with two agents, show that every truthful mechanism with two agents admits an emph{efficiency ratio} of $0$, and derive a large family of emph{strictly truthful}, emph{envy-free (EF)}, and emph{proportional} mechanisms for an arbitrary number of agents. Finally, for indivisible chores with an arbitrary number of agents having emph{bi-valued} cost functions, we give an emph{ex-ante} truthful, ex-ante emph{Pareto optimal}, ex-ante EF, and emph{ex-post envy-free up to one item} mechanism, improving the best guarantees for bi-valued instances by prior works.

Problem

• Comparing truthful allocation mechanisms for goods versus chores.
• Characterizing truthful mechanisms for indivisible chores with two agents.
• Developing efficient and fair mechanisms for divisible chores with multiple agents.

Innovation

• Bundle-swapping transforms goods properties to chores
• Generalized transformation for divisible chores mechanisms
• Ex-ante truthful mechanism for bi-valued cost functions