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arXiv · 2308.11230

Towards Optimal Subsidy Bounds for Envy-freeable Allocations

Yasushi Kawase·Kazuhisa Makino·Hanna Sumita·Akihisa Tamura·Makoto Yokoo
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Abstract

We study the fair division of indivisible items with subsidies among $n$ agents, where the absolute marginal valuation of each item is at most one. Under monotone valuations (where each item is a good), Brustle et al. (2020) demonstrated that a maximum subsidy of $2(n-1)$ and a total subsidy of $2(n-1)^2$ are sufficient to guarantee the existence of an envy-freeable allocation. In this paper, we improve upon these bounds, even in a wider model. Namely, we show that, given an EF1 allocation, we can compute in polynomial time an envy-free allocation with a subsidy of at most $n-1$ per agent and a total subsidy of at most $n(n-1)/2$. Moreover, we present further improved bounds for monotone valuations.

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Yasushi Kawase, Kazuhisa Makino, Hanna Sumita, Akihisa Tamura, Makoto Yokoo. 2023-08-22. Towards Optimal Subsidy Bounds for Envy-freeable Allocations. https://arxiv.org/abs/2308.11230

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