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We present necessary and sufficient conditions for the existence of such prices for decentralized market problems where market participants have integral decision variables and their feasible sets are given in complete linear description. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications. Furthermore, we compute competitive equilibria for two classes of decentralized market problems arising in energy markets and show that competitive equilibria may exist regardless of integralities.<\/jats:p>","DOI":"10.1007\/s00186-022-00775-z","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T02:05:32Z","timestamp":1648519532000},"page":"451-474","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Exploiting complete linear descriptions for decentralized power market problems with integralities"],"prefix":"10.1007","volume":"95","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5990-0324","authenticated-orcid":false,"given":"Lukas","family":"H\u00fcmbs","sequence":"first","affiliation":[]},{"given":"Alexander","family":"Martin","sequence":"additional","affiliation":[]},{"given":"Lars","family":"Schewe","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,26]]},"reference":[{"issue":"2","key":"775_CR1","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1016\/j.ejor.2011.05.009","volume":"214","author":"V Araoz","year":"2011","unstructured":"Araoz V, J\u00f6rnsten K (2011) Semi-Lagrangean approach for price discovery in markets with non-convexities. 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