Truthful-in-Expectation Mechanism with Constant Maximin-Share Guarantee

2026-09-28

AI Summary

This study addresses the challenge of allocating indivisible items, where existing mechanisms struggle to simultaneously achieve strategy-proofness and fairness, with maximin share (MMS) guarantees constrained by logarithmic lower bounds. Leveraging verified cardinal information, this work proposes a polynomial-time mechanism that generates an initial solution via fractional allocation rules and employs balanced edge coloring and graph matching techniques for probabilistic decomposition, thereby ensuring expected truthfulness. The primary contribution lies in breaking the logarithmic barrier by achieving, for the first time, a constant 1/7 MMS approximation guarantee alongside ex-ante envy-freeness. This establishes a new paradigm for the fair allocation of resources among strategic agents, offering both theoretical optimality and computational efficiency.

Abstract

We study the truthful and fair allocation of indivisible goods to $n$ strategic agents with additive valuations. Babaioff, Feige, and Manaker Morag [FOCS 2026] gave a randomized mechanism that uses only the agents'rankings of the goods, is truthful in expectation (TIE), and guarantees every agent $1/(H_{n-1}+2)=\Theta(1/\log n)$ of her maximin share (MMS) in every realized allocation, where $H_{n-1}$ is the $(n-1)$th harmonic number; this is nearly the best possible with rankings alone. They conjectured that cardinal information allows TIE mechanisms to achieve a constant ex-post MMS guarantee. We confirm this conjecture: our TIE mechanism guarantees every agent at least $1/7$ of her MMS in every realized allocation; moreover, the mechanism is ex-ante envy-free and can be implemented in polynomial time. Our mechanism has two key technical ingredients, both of which may be of independent interest. The first is a truthful fractional allocation rule specifying each agent's probability of receiving each good: it favors each agent on her top $n-1$ goods and reduces her probability of receiving a good for each other agent who also ranks it among her top $n-1$ goods. The second is the balanced edge coloring: we decompose these probabilities into equally likely matchings from agents to high-value goods, those that alone meet an agent's guarantee, and balance these matchings in a fine-grained way without changing any marginal probability, so that every agent who receives no high-value good can obtain sufficient value from the remaining goods without over-allocating any good.

Problem

• indivisible goods allocation
• truthful-in-expectation mechanism
• maximin share guarantee
• strategic agents
• fair division

Innovation

• Truthful-in-Expectation Mechanism
• Maximin-Share Guarantee
• Fractional Allocation Rule
• Balanced Edge Coloring
• Indivisible Goods