TL;DR
This paper investigates the problem of allocating indivisible items among agents in a graph-based valuation model, providing new results on the fairness of maximin share allocations for various valuation types.
Contribution
It introduces new positive and negative results for approximate MMS and PMMS fairness in the graphical valuation model across different valuation classes.
Findings
Positive results for MMS fairness in certain graph settings.
Negative results indicating limitations of MMS approximations.
Extension of fairness analysis to XOS and subadditive valuations.
Abstract
We study the problem of (approximate) maximin share (MMS) allocation of indivisible items among a set of agents. We focus on the graphical valuation model, previously studied by Christodolou, Fiat, Koutsoupias, and Sgouritsa ("Fair allocation in graphs", EC 2023), where the input is given by a graph where edges correspond to items, and vertices correspond to agents. An edge may have non-zero marginal value only for its incident vertices. We study additive, XOS and subadditive valuations and we present positive and negative results for (approximate) MMS fairness, and also for (approximate) pair-wise maximin share (PMMS) fairness.
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