On fair division of a homogeneous good

We consider the problem of dividing a homogeneous divisible good among n players. Each player holds a private non-negative utility function that depends only on the amount of the good that he receives. We define the fair share of a player P to be the average utility that a player could receive if all players had the same utility function as P. We present a randomized allocation mechanism in which every player has a dominant strategy for maximizing his expected utility. Every player that follows his dominant strategy is guaranteed to receive an expected utility of at least n/(2. n - 1) of his fair share. This is best possible in the sense that there is a collection of utility functions with respect to which no allocation mechanism can guarantee a larger fraction of the fair share. In interesting special cases our allocation mechanism does offer a larger fraction of the fair share.