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We prove that an assignment game is PMAS-admissible if and only if the positive elements of the underlying nonnegative matrix form orthogonal submatrices of three special types. In game theoretic terms it means that an assignment game is PMAS-admissible if and only if it contains either a veto player or a dominant veto mixed pair, or the game is a composition of these two types of special assignment games. We also show that in PMAS-admissible assignment games all core allocations can be extended to a PMAS, and the nucleolus coincides with the tau-value.<\/jats:p>","DOI":"10.1007\/s00355-023-01477-z","type":"journal-article","created":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T05:02:03Z","timestamp":1692594123000},"page":"67-88","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Assignment games with population monotonic allocation schemes"],"prefix":"10.1007","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2447-3219","authenticated-orcid":false,"given":"Tam\u00e1s","family":"Solymosi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,21]]},"reference":[{"key":"1477_CR1","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s00355-019-01197-3","volume":"53","author":"T Abe","year":"2019","unstructured":"Abe T, Liu S (2019) Monotonic core allocation paths for assignment games. 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