Fair Division with Prioritized Agents

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 envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In EF1 allocation, agent envy others' allocated shares, but only item. many applications, we wish specify subset prioritized agents where strict needs be guaranteed from these remaining agents, while ensuring whole still EF1. Prioritized those who are envious in previous belong underrepresented groups, etc. Motivated by this, propose new fairness notion named with EFprior, study existence algorithmic aspects for computing EFprior allocation. With additive valuations, simple round-robin algorithm able compute this paper, mainly focus on general valuations. particular, present polynomial-time outputs most items allocated. When all need allocated, also algorithms some well-motivated special cases.