Allocating Contiguous Blocks of Indivisible Chores Fairly: Revisited

Ankang Sun, Bo Li

Abstract: Resource allocation is a fundamental problem in multi-agent systems, with two key factors to consider: fairness and efficiency. The concept of the "price of fairness'' helps in the understanding of efficiency loss under fairness constraints. Among the diverse resource allocation settings, cake cutting stands out as a prominent model. Recently, Hö hne and van Stee [Inf. Comput., 2021] examined a variation of this model in which the cake represents indivisible chores, with each agent requiring a connected piece of the chores. Hö hne and van Stee provided upper and lower bounds on the price of fairness when fairness is measured by envy-freeness and proportionality. However, in the case of indivisible items, achieving envy-free and proportional allocations is difficult, rendering these bounds insufficient for a comprehensive understanding of the true trade-off between fairness and efficiency. In this paper, we revisit the same problem and consider fairness notions that are satisfiable, including proportionality up to one item, and maximin share fairness. By presenting tight bounds on the price of fairness with respect to these notions, we complete the picture of fairness and efficiency trade-off.