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Our models enrich concurrent game models with payoffs and guards on actions associated with each state of the model and propose a quantitative extension of the logic $${\\textsf {ATL}}^{*}$$<\/jats:tex-math>\n \n \n ATL<\/mml:mi>\n <\/mml:mrow>\n \n \n \u2217<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that enables the combination of quantitative and qualitative reasoning. We illustrate the framework with some detailed examples. Finally, we consider the model-checking problems arising in our framework and establish some general undecidability and decidability results for them.<\/jats:p>","DOI":"10.1007\/s10458-021-09531-9","type":"journal-article","created":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T06:08:56Z","timestamp":1636438136000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Combining quantitative and qualitative reasoning in concurrent multi-player games"],"prefix":"10.1007","volume":"36","author":[{"given":"Nils","family":"Bulling","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0157-1644","authenticated-orcid":false,"given":"Valentin","family":"Goranko","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,9]]},"reference":[{"key":"9531_CR1","doi-asserted-by":"crossref","unstructured":"Alechina, N., Demri, S., & Logan, B. (2020). 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