Fair Division with Weighted and Prioritized Agents

We consider the fair division problem with prioritized and weighted agents. It has been shown that envy-free (EF) allocation may not exist, but its relaxed version envy-freeness up to one item (EF1) and weighted envy-freeness up to one item (WEF1) have been widely considered. First, a subset of agents is designated as priority agents, which may be the envious agents from previous allocations, and weights can quantify the rights of agents in allocating items. Motivated by this, we propose a new fairness notion named weight envy-freeness with prioritized agents \((WEF_{PRIOR})\) , which requires that prioritized agents do not envy non-prioritized agents, while the entire allocation is WEF1. We study the existence of \(WEF_{PRIOR}\) allocation, which can be computed by the weighted version of the Round-Robin algorithm when the valuations of agents are additive.