Strategy-proof Sharing

We consider the problem of sharing a divisible good, where agents prefer more to less. First, 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 in a manner that is consistent with quasi-constancy, we provide a way to find every strategy-proof sharing rule. Finally, we identify a necessary and sufficient condition for the existence of non-constant, strategy-proof sharing rules, by examining the relationship between the constancy of strategy-proof sharing rules and the dimension of the solution space of the linear system.