Getting More by Knowing Less: Bayesian Incentive Compatible Mechanisms for Fair Division

We study fair resource allocation with strategic agents. It is well-known that, across multiple fundamental problems in this domain, truthfulness and fairness are incompatible. For example, when allocating indivisible goods, there is no truthful and deterministic mechanism that guarantees envy-freeness up to one item (EF1), even for two agents with additive valuations. Or, in cake-cutting, no truthful and deterministic mechanism always outputs a proportional allocation, even for two agents with piecewise-constant valuations. Our work stems from the observation that, in the context of fair division, truthfulness is used as a synonym for Dominant Strategy Incentive Compatibility (DSIC), requiring that an agent prefers reporting the truth, no matter what other agents report. In this paper, we instead focus on Bayesian Incentive Compatible (BIC) mechanisms, requiring that agents are better off reporting the truth in expectation over other agents' reports. We prove that, when agents know a bit less about each other, a lot more is possible: using BIC mechanisms we can overcome the aforementioned barriers that DSIC mechanisms face in both the fundamental problems of allocation of indivisible goods and cake-cutting. We prove that this is the case even for an arbitrary number of agents, as long as the agents' priors about each others' types satisfy a neutrality condition. En route to our results on BIC mechanisms, we also strengthen the state of the art in terms of negative results for DSIC mechanisms.