Bayesian Fair Division: Truthfulness in Picking Sequence with Correlated Valuations

2026-08-07

AI Summary

This study investigates whether sequential allocation mechanisms can incentivize truthful preference reporting under a Bayesian fairness framework when agents’ valuations are partially observable and positively correlated. Leveraging Bayesian game analysis, mechanism design theory, and probabilistic modeling of correlation, the work establishes that with two agents, positive correlation alone is sufficient to render truth-telling a Bayesian Nash equilibrium. However, this property fails to extend to settings with three or more agents, where the authors uncover a novel form of strategic manipulation. The findings delineate precise conditions under which sequential mechanisms guarantee truthfulness in the two-agent case while exposing their inherent limitations in multi-agent environments.

Abstract

Sequential allocation mechanisms contain a class of widely studied mechanisms (e.g., round-robin) in the fair division of indivisible goods, where agents take turns picking items in a predefined picking order. It is known that the sequential allocation mechanisms are not truthful: when an agent's most preferred item is not valued by others, the agent may manipulate the mechanism by choosing to defer picking that item and instead competing for another slightly less preferred item that is valued by others. Two underlying reasons are that each agent has perfect knowledge of the others' valuations, and each item's value to each agent can differ significantly. Will the mechanism be more truthful when each agent only has partial information about the others' valuations, which are known to be roughly consistent? This naturally motivates the study of the Bayesian fair division model. In this paper, we answer this question affirmatively for two agents. Under the Bayesian model, we precisely characterize the extent of this ``rough consistency'' that incentivizes agents' truth-telling. In particular, we show that for the case of two agents, when the valuations are positively correlated, truth-telling forms a Bayesian Nash equilibrium under the sequential allocation mechanisms. However, we show that truthfulness fails to extend to the setting with more than two agents. For more than two agents, we reveal a new type of manipulation that is different from the above-mentioned manipulation that defers a highly valued but less competitive item. Our result reveals a fundamental limitation on the truthfulness of sequential mechanisms.

Problem

• Bayesian fair division
• truthfulness
• sequential allocation
• correlated valuations
• indivisible goods

Innovation

• Bayesian fair division
• truthfulness
• sequential allocation
• correlated valuations
• Bayesian Nash equilibrium