Equitability and welfare maximization for allocating indivisible items

Abstract We study fair allocations of indivisible goods and chores in conjunction with system efficiency, measured by two social welfare functions, namely utilitarian egalitarian welfare. To model preference, each agent is associated a cardinal additive valuation function. The fairness criteria we are concerned equitability up to any item (EQX) one (EQ1). For the trade-off between investigate efficiency loss under these constraints establish price fairness. From computational perspective, provide complete picture complexity (i) deciding existence an EQX/EQ1 welfare-maximizing allocation; (ii) computing maximizer among all allocations.