Research demonstrates computing envy-free Pareto-efficient allocations in fair allocation games, suggesting effective methods for diverse preferences.
We study the problems of computing envy-free Pareto-efficient allocations in the context of fair allocation and hedonic games under dichotomous preferences. We establish Σp2-completeness of deciding the existence of envy-free Pareto-efficient allocations, refining earlier related results. We also develop iterative SAT-based exact algorithms for computing envy-free Pareto-efficient allocations, and extend the approach to computing minimum-envy Pareto-efficient allocations under different combinations of aggregation functions. We provide open-source implementations of the algorithms and show empirically that the approach scales to computing envy-free Pareto-efficient allocations up to hundreds of agents.
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Conati et al. (2025) studied this question.
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