  We study fair allocation of indivisible goods to agents with unequal
entitlements. Fair allocation has been the subject of many studies in both
divisible and indivisible settings. Our emphasis is on the case where the goods
are indivisible and agents have unequal entitlements. This problem is a
generalization of the work by Procaccia and Wang wherein the agents are assumed
to be symmetric with respect to their entitlements. Although Procaccia and Wang
show an almost fair (constant approximation) allocation exists in their
setting, our main result is in sharp contrast to their observation. We show
that, in some cases with $n$ agents, no allocation can guarantee better than
$1/n$ approximation of a fair allocation when the entitlements are not
necessarily equal. Furthermore, we devise a simple algorithm that ensures a
$1/n$ approximation guarantee. Our second result is for a restricted version of
the problem where the valuation of every agent for each good is bounded by the
total value he wishes to receive in a fair allocation. Although this assumption
might seem w.l.o.g, we show it enables us to find a $1/2$ approximation fair
allocation via a greedy algorithm. Finally, we run some experiments on
real-world data and show that, in practice, a fair allocation is likely to
exist. We also support our experiments by showing positive results for two
stochastic variants of the problem, namely stochastic agents and stochastic
items.
