Non-Monotonicity in Fair Division of Graphs

Abstract

We consider the problem of fairly allocating the vertices of a graph among n agents, where the value of a bundle is determined by its cut value---the number of edges with exactly one endpoint in the bundle. This model naturally captures applications such as team formation and network partitioning, where valuations are inherently non-monotonic: the marginal values may be positive, negative, or zero depending on the composition of the bundle. We focus on the fairness notion of envy-freeness up to one item (EF1) and explore its compatibility with several efficiency concepts such as Transfer Stability (TS) that prohibits any transfer of item that benefit one agent at another