Envy-free house allocation with minimum subsidy

Key Points

An envy-free allocation can be achieved with minimum subsidy under certain conditions.
The outcome reveals that computing such allocations is NP-hard unless agents have identical utilities.
Finding an allocation becomes efficient when the number of houses differs from the agents by a constant value or when utilities align uniformly among agents—this creates a simpler allocation scenario for them overall. A standard analysis highlights multiple complexities in resource distribution; more research is warranted.

Abstract

House allocation refers to the problem where m houses are to be allocated to n agents so that each agent receives one house. Since an envy-free house allocation does not always exist, we consider finding such an allocation in the presence of subsidy. We show that computing an envy-free allocation with minimum subsidy is NP-hard in general, but can be done efficiently if m differs from n by an additive constant or if the agents have identical utilities.

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Cite This Study

Choo et al. (Sat,) studied this question.

synapsesocial.com/papers/68e7603ab6db6435876d6972 https://doi.org/https://doi.org/10.1016/j.orl.2024.107103

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