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This leads to economic interpretable conditions on the demand distribution under which such fixed points exist and are unique. We find that markets with increasing price elasticity of expected demand that eventually become elastic correspond to distributions with <jats:italic>decreasing generalized mean residual life<\/jats:italic> (DGMRL) and finite second moment. DGMRL distributions strictly generalize the widely used <jats:italic>increasing generalized failure rate<\/jats:italic> (IGFR) distributions. We further elaborate on the relationship of the two classes, link their limiting behavior at infinity and examine moment and closure properties of DGMRL distributions that are important in economic applications. The DGMRL unimodality condition is useful in the analysis of optimal decisions under uncertainty in settings that are not covered by the widely-used IGFR condition; thus, it can be of broader interest to the game-theory and operations research literature.<\/jats:p>","DOI":"10.1007\/s10479-023-05425-z","type":"journal-article","created":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T17:01:46Z","timestamp":1686157306000},"page":"1661-1679","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A generalization of the increasing generalized failure rate unimodality condition"],"prefix":"10.1007","volume":"336","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1498-1490","authenticated-orcid":false,"given":"Stefanos","family":"Leonardos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Constandina","family":"Koki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Costis","family":"Melolidakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,7]]},"reference":[{"issue":"2","key":"5425_CR1","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/s00199-004-0514-4","volume":"26","author":"M Bagnoli","year":"2005","unstructured":"Bagnoli, M., & Bergstrom, T. 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