Externalities in cake cutting

The cake cutting problem models the fair division of a heterogeneous good between multiple agents. Previous work assumes that each agent derives value only from its own piece. However, agents may also care about the pieces assigned to other agents; such externalities naturally arise in fair division settings. We extend the classical model to capture externalities, and generalize the classical fairness notions of proportionality and envyfreeness. Our technical results characterize the relationship between these generalized properties, establish the existence or nonexistence of fair allocations, and explore the computational feasibility of fairness in the face of externalities.