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 envy-freeness. 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.