Abstract

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).

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