Fair Allocation of Items

Abstract

We study the problem of fair allocation of items / goods / resources to m agents. The problem appears in two broad variants: (a) fair allocation of a divisible item wherein one item is to be divided amongst m agents; the problem is popularly known as cake-cutting problem, (b) fair allocation of indivisible items wherein n indivisible or non-shareable items are to be allocated amongst m agents. Further, the item/items can be homogeneous or heterogeneous. Both the variants have several real-time applications such as land-division amongst heirs is an example of allocation of a divisible item, whereas in divorce settlement, division of assets such as house, car, artifacts, etc. is an example of allocation of indivisible items. There are many notions of fairness and social welfare that are important and have been studied: envy-freeness, proportionality, Pareto optimality, maximin share guarantee, Borda maximin share guarantee, utilitarian social welfare, egalitarian social welfare and Nash social welfare. In this chapter, we discuss about the fair-allocation problem and their related results.