Reproduce “Generalized Rental Harmony” on OpenResearch
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About this paper
Erel Segal-Halevi
Erel Segal-Halevi's research unifies diverse models of tenant preferences in the rental harmony problem, demonstrating that a single mathematical technique, Sperner's Lemma, proves the existence of envy-free allocations for 'compensable tenants,' a class encompassing quasilinear and miserly preferences. This work extends prior results on complex scenarios like roommates and secretive agents to this generalized preference model.
Key insights
- Sperner's Lemma can serve as a universal tool for proving the existence of envy-free allocations in rental harmony problems, even for diverse and complex tenant preference models, by carefully reinterpreting how simplex points map to price vectors.
- The 'compensable tenants' model provides a unified framework that subsumes previously distinct preference models like quasilinear, Archimedean, and miserly tenants, bridging a theoretical gap in fair division research.
- The applicability of Sperner-type combinatorial arguments extends to proving existence for envy-free allocations in complex scenarios, such as those involving roommates, secretive agents, or extra agents, under generalized preference assumptions.
Summary by alphaXiv.
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