Weighted Envy-freeness in Indivisible Item Allocation

We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. propose two variants weighted envy-freeness up to one item (WEF1): strong , where envy can be eliminated by removing an from envied agent’s bundle, weak either (as version) or replicating bundle envying bundle. show additive valuations, is both Pareto optimal strongly WEF1 always exists computed pseudo-polynomial time; moreover, maximizes Nash social welfare may not WEF1, but it satisfies version property. Moreover, we establish a generalization round-robin picking sequence algorithm produces polynomial time arbitrary number agents; agents, efficiently achieve optimality adapting adjusted winner procedure. Our work highlights several aspects which fair division richer more challenging than its unweighted counterpart.