On Fair and Efficient Allocations of Indivisible Goods

We study the problem of fair and efficient allocation a set indivisible goods to agents with additive valuations using popular fairness notions envy-freeness up one good (EF1) equitability (EQ1) in conjunction Pareto-optimality (PO). There exists pseudo-polynomial time algorithm compute an EF1+PO allocation, non-constructive proof existence allocations that are both EF1 fractionally Pareto-optimal (fPO). present EF1+fPO thereby improving earlier results. Our techniques also enable us show EQ1+fPO always when values positive, it can be computed time. consider class k-ary instances where k is constant, i.e., each agent has at most different for goods. such polynomial When all we Next, number (also EQ1+PO) These results significantly extend polynomial-time computability beyond known cases binary or identical valuations. Further, computing reduces complexity PLS. design computes Nash welfare maximizing there constantly many constant