Towards Optimal Subsidy Bounds for Envy-freeable Allocations

08/22/2023

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by   Yasushi Kawase, et al.

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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.