Designing Truthful Mechanisms for Asymptotic Fair Division

2025-12-11

AI Summary

This paper addresses mechanism design for strategy-proof fair allocation in the progressive fairness setting: allocating $m$ indivisible items to $n$ strategic agents whose valuations follow a generalized joint distribution—allowing correlations, atomic support, and non-uniform maximum values—with the goal of achieving envy-freeness with high probability. We propose the first truthful-in-expectation randomized mechanism applicable to *any* “well-behaved” joint valuation distribution, overcoming the prior restriction to i.i.d. assumptions. Our framework extends naturally to weighted fairness and settings with multiple agent or item types. When $m = Omega(n log n)$, the mechanism outputs an envy-free allocation with high probability, while guaranteeing truthfulness in expectation and polynomial-time computability. This resolves an open problem posed by Manurangsi & Suksompong (2017).

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Data transparency and provenance

Abstract

We study the problem of fairly allocating a set of $m$ goods among $n$ agents in the asymptotic setting, where each item's value for each agent is drawn from an underlying joint distribution. Prior works have shown that if this distribution is well-behaved, then an envy-free allocation exists with high probability when $m=Omega(nlog{n})$ [Dickerson et al., 2014]. Under the stronger assumption that item values are independently and identically distributed (i.i.d.) across agents, this requirement improves to $m=Omega(nlog{n}/log{log{n}})$, which is tight [Manurangsi and Suksompong, 2021]. However, these results rely on non-strategyproof mechanisms, such as maximum-welfare allocation or the round-robin algorithm, limiting their applicability in settings with strategic agents. In this work, we extend the theory to a broader, more realistic class of joint value distributions, allowing for correlations among agents, atomicity, and unequal probabilities of having the highest value for an item. We show that envy-free allocations continue to exist with a high probability when $m=Omega(nlog{n})$. More importantly, we give a new randomized mechanism that is truthful in expectation, efficiently implementable in polynomial time, and outputs envy-free allocations with high probability, answering an open question posed by [Manurangsi and Suksompong, 2017]. We further extend our mechanism to settings with asymptotic weighted fair division and multiple agent types and good types, proving new results in each case.

Problem

• Design truthful mechanisms for asymptotic fair division with correlated values
• Extend envy-free existence to broader joint distributions beyond i.i.d.
• Provide efficient randomized mechanisms for strategic agents in fair allocation

Innovation

• Truthful randomized mechanism for envy-free allocation
• Extends to correlated distributions and strategic agents
• Polynomial-time implementation with high probability guarantees