Superadditivity and Subadditivity in Fair Division

  •  Rishi Mirchandani    


I examine the classic problem of fair division of a piecewise homogeneous good.  Previous work developed algorithms satisfying various combinations of fairness notions (such as proportionality, envy-freeness, equitability, and Pareto-optimality).  However, this previous work assumed that all utility functions are additive.  Recognizing that additive functions accurately model utility only in certain situations, I investigate superadditive and subadditive utility functions.  Next, I propose a new division protocol that utilizes nonlinear programming and test it on a sample instance.  Finally, I prove theoretical results that address (a) relationships between fairness notions, and (b) the orthogonal issue of division efficiency (i.e., the price of satisfying particular fairness notions).

This work is licensed under a Creative Commons Attribution 4.0 License.