Weighted Envy-free Allocation with Subsidy

We consider the problem of fair allocation of indivisible items with subsidies when agents have weighted entitlements. After highlighting several important differences from the unweighted case, we present several results concerning weighted envy-freeability including general characterizations, algorithms for achieving and testing weighted envy-freeability, lower and upper bounds of the amount of subsidies for envy-freeable allocations, and algorithms for achieving weighted envy-freeability along with other properties.