This randomized technique discovers minimum subsidy needed for envy-free house allocation among agents, implying feasibility under specific conditions.
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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Choo et al. (2024) studied this question.
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