Balancing Fairness and Efficiency in the Allocation of Indivisible Goods

The allocation of indivisible goods is a ubiquitous problem, and two main objectives are fairness and efficiency. Depending on the fairness and efficiency benchmarks used, these objectives can be aligned or conflicting with each other. We study the degree of compatibility between certain fairness and efficiency notions in two different ways. First, we investigate the egalitarian prices of several fairness properties and compare them to their utilitarian prices. Secondly, we characterise all additive welfarist rules guaranteeing envy-freeness up to one good (EF1) for different classes of instances.