  We consider the fair division problem of indivisible items. It is well-known
that an envy-free allocation may not exist, and a relaxed version of
envy-freeness, envy-freeness up to one item (EF1), has been widely considered.
In an EF1 allocation, an agent may envy others' allocated shares, but only up
to one item. In many applications, we may wish to specify a subset of
prioritized agents where strict envy-freeness needs to be guaranteed from these
agents to the remaining agents, while ensuring the whole allocation is still
EF1. Prioritized agents may be those agents who are envious in a previous EF1
allocation, those agents who belong to underrepresented groups, etc. Motivated
by this, we propose a new fairness notion named envy-freeness with prioritized
agents "EFPrior", and study the existence and the algorithmic aspects for the
problem of computing an EFPrior allocation. With additive valuations, the
simple round-robin algorithm is able to compute an EFPrior allocation. In this
paper, we mainly focus on general valuations. In particular, we present a
polynomial-time algorithm that outputs an EFPrior allocation with most of the
items allocated. When all the items need to be allocated, we also present
polynomial-time algorithms for some well-motivated special cases.
