Fair Division with Market Values

TL;DR

This paper introduces a new model of fair division incorporating market values, explores fairness guarantees under subjective and market valuations, and extends the framework to non-additive valuations and cake-cutting.

Contribution

It presents a novel model combining subjective and market valuations for fair division, analyzes fairness guarantees, and extends the approach to non-additive valuations and cake-cutting.

Findings

SD-EF1 with respect to both valuations may not exist

EF1 with subjective and SD-EF1 with market valuation can be guaranteed

Extended model to non-additive valuations and cake-cutting

Abstract

We introduce a model of fair division with market values, where indivisible goods must be partitioned among agents with (additive) subjective valuations, and each good additionally has a market value. The market valuation can be viewed as a separate additive valuation that holds identically across all the agents. We seek allocations that are simultaneously fair with respect to the subjective valuations and with respect to the market valuation. We show that an allocation that satisfies stochastically-dominant envy-freeness up to one good (SD-EF1) with respect to both the subjective valuations and the market valuation does not always exist, but the weaker guarantee of EF1 with respect to the subjective valuations along with SD-EF1 with respect to the market valuation can be guaranteed. We also study a number of other guarantees such as Pareto optimality, EFX, and MMS. In addition, we explore non-additive valuations and extend our model to cake-cutting. Along the way, we identify several tantalizing open questions.