Bayesian fair division: truthfulness holds for 2 agents, collapses at 3

Sequential allocation mechanisms—like the classic round-robin where agents take turns picking items—are widely used in fair division of indivisible goods. But they're known to be manipulable: when an agent's top choice isn't valued by others, they may strategically defer it and chase a slightly less preferred item that others also want. This happens because agents have perfect knowledge of each other's valuations. In a new paper on arXiv (2608.07414), Xiaolin Bu and Biaoshuai Tao ask a natural question: what happens when agents only have partial information about others' valuations, which are known to be "roughly consistent"?

Under the Bayesian fair-division model, the authors give a crisp answer for the two-agent case: when valuations are positively correlated, truth-telling forms a Bayesian Nash equilibrium. They precisely characterize the degree of "rough consistency" needed to keep agents honest. But the good news ends there. For more than two agents, truthfulness breaks down, and the paper uncovers a novel manipulation type that is distinct from the classic "defer a highly valued but less competitive item" trick. This reveals a fundamental limitation: the incentive-compatibility of sequential mechanisms depends heavily on the number of participants and the correlation structure of their preferences—a crucial insight for designing allocation protocols in multi-agent systems.