Truthful-in-Expectation MMS Allocations for Chores

2026-09-28

AI Summary

This study addresses the challenge that existing ex-ante truthful mechanisms for indivisible chore allocation fail to achieve constant ex-post maximin share (MMS) approximation guarantees. By integrating game-theoretic mechanism design with combinatorial optimization analysis, this work proposes the first chore allocation mechanism that simultaneously satisfies ex-ante truthfulness and achieves a constant ex-post MMS approximation. The contribution is threefold: it establishes, for the first time, a constant ex-post MMS approximation ratio for an arbitrary number of agents, yielding a general approximation ratio of 1.97; it tightens the lower bound for two agents to 4/3 and proves its optimality; and it attains a ratio of 3/2 for three agents while establishing a theoretical lower bound of 13/12 for any n ≥ 3 agents.

Abstract

We study truthful-in-expectation (TIE) mechanisms for allocating indivisible chores alongside ex-post maximin share (MMS) guarantees. For goods, Bu and Tao (FOCS 2025) established a (1/n)-approximation for TIE mechanisms, and this was substantially improved by Babaioff, Feige, and Manaker Morag (FOCS 2026), who established an \Omega(1/\log n) approximation, where n is the number of agents. The corresponding problem for chores has received less attention. The best-known result is due to Aziz, Li, and Wu (MAPR 2024), who gave a TIE mechanism with an O(\sqrt{\log n}) MMS approximation guarantee that holds only in expectation. They also established a 6/5 lower bound for TIE mechanisms for two agents. In this paper, we present the first TIE mechanism for chores that achieves a constant ex-post MMS approximation guarantee. Specifically, our mechanism guarantees an ex-post ratio of 1.97 for any number of agents n, which improves to 4/3 for n=2 and 3/2 for n=3. On the hardness side, we tighten the two-agent lower bound to 4/3, showing that our mechanism is optimal for n=2. More generally, we establish a lower bound of 13/12 on the ex-post MMS approximation ratio achievable by TIE mechanisms for every n\ge 3.

Problem

• truthful-in-expectation mechanisms
• maximin share
• indivisible chores
• fair division
• approximation guarantee

Innovation

• Truthful-in-Expectation Mechanism
• Maximin Share Approximation
• Indivisible Chores Allocation
• Ex-post Guarantee
• Mechanism Design