Fair allocation of combinations of indivisible goods and chores

07/27/2018

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by   Haris Aziz, et al.

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We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are "goods" i.e., they yield positive utility for the agents. There is also some work where the items are "chores" that yield negative utility for the agents. In this work, we consider more general scenarios where for any item, an agent may have negative or positive utility for it. We show that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We also point out several gaps in the literature regarding the existence of allocations satisfying certain fairness and efficiency properties as well as the computational complexity of computing such allocations.