Bayesian Fair Division: Truthfulness in Picking Sequence with Correlated Valuations

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.