Dividing Connected Chores Fairly

In this paper we consider the fair division of chores (tasks that need to be performed by agents, with negative utility for them), and study the loss in social welfare due to fairness. Previous work has been done on this so-called price of fairness, concerning fair division of cakes and chores with non-connected pieces and of cakes with connected pieces. We provide tight or nearly tight bounds on the price of fairness in situations where each player has to receive one connected piece of the chores. We also give the first proof of the existence of equitable divisions for chores with connected pieces.