Communication Complexity of Discrete Fair Division

TL;DR

This paper thoroughly investigates the communication complexity involved in fair division of indivisible goods, providing complete classifications for various fairness notions, valuation classes, and protocol types, resolving key open questions.

Contribution

It offers a comprehensive analysis that determines whether computing fair allocations is polynomial or exponential in communication complexity across multiple scenarios.

Findings

Complete classification of communication complexity for fair division

Polynomial vs exponential bounds established for all cases

Results apply to both deterministic and randomized protocols

Abstract

We initiate the study of the communication complexity of fair division with indivisible goods. We focus on some of the most well-studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive and unrestricted). Within these parameters, our results completely resolve whether the communication complexity of computing a fair allocation (or determining that none exist) is polynomial or exponential (in the number of goods), for every combination of fairness notion, valuation class, and number of players, for both deterministic and randomized protocols.