Fair Division with Market Values
This addresses fairness in resource allocation for scenarios like auctions or inheritance where objective market values matter, but it is incremental as it builds on existing fair division models.
The paper tackles the problem of fair division when goods have both subjective and market values, showing that an allocation satisfying strong fairness criteria (SD-EF1) for both valuations does not always exist, but a weaker guarantee (EF1 for subjective and SD-EF1 for market) can be achieved.
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.