Strategy-Proof Sharing

We consider the problem of sharing a good, where agents prefer more to less. In this environment, we prove that a sharing rule satisfies strategy-proofness if and only if it has the quasi-constancy property: no one changes her own share by changing her announcements. Next by constructing a system of linear equations, we provide a way to find all of the strategy-proof sharing rules, and identify a necessary and sufficient condition for the existence of a non-constant, strategy-proof sharing rule. Finally, we show that it is only the equal sharing rule that satisfies strategy-proofness and symmetry.