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If the resource is one-dimensional, the known results from the NDG literature are recovered: either the Nash solution is uniquely supported at the perturbations\u2019 limit, or the entire (relative interior of the) Pareto frontier is supported; which case obtains depends on the type of perturbation. I show that, contrary to the prominence of the Nash solution under smoothing in the utility space, the entire frontier can be supported under a variety of economically-plausible perturbations. The case where the resource is multi-dimensional is qualitatively different.<\/jats:p>","DOI":"10.1007\/s00182-025-00941-7","type":"journal-article","created":{"date-parts":[[2025,5,24]],"date-time":"2025-05-24T09:00:42Z","timestamp":1748077242000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Nash\u2019s demand game and resource-allocation"],"prefix":"10.1007","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7677-6719","authenticated-orcid":false,"given":"Shiran","family":"Rachmilevitch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,24]]},"reference":[{"key":"941_CR1","doi-asserted-by":"publisher","first-page":"1641","DOI":"10.3982\/ECTA11711","volume":"83","author":"D Abreu","year":"2015","unstructured":"Abreu D, Pearce D (2015) A dynamic reinterpretation of Nash bargaining with endogenous threats. 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