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While integral games have been considered in the literature before, no polynomial time algorithm computing an equilibrium was known. Also for this class, we devise the first polynomial time algorithm and use it as a building block for our main algorithm. We then develop a polynomial time computable transformation mapping a multimarket Cournot competition game with firm-specific affine price functions and quadratic costs to an associated atomic splittable congestion game as described above. The transformation preserves equilibria in either game and, thus, leads \u2013 via our first algorithm \u2013 to a polynomial time algorithm computing Cournot equilibria. Finally, our analysis for integrally-splittable games implies new bounds on the difference between real and integral Cournot equilibria. The bounds can be seen as a generalization of the recent bounds for single market oligopolies obtained by Todd (Math Op Res 41(3):1125\u20131134 2016,\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"doi\" xlink:href=\"https:\/\/doi.org\/10.1287\/moor.2015.0771\">10.1287\/moor.2015.0771<\/jats:ext-link>\n                    ).\n                  <\/jats:p>","DOI":"10.1007\/s10107-020-01604-z","type":"journal-article","created":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T04:08:48Z","timestamp":1613707728000},"page":"1-34","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Equilibrium computation in resource allocation games"],"prefix":"10.1007","volume":"194","author":[{"given":"Tobias","family":"Harks","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8768-7973","authenticated-orcid":false,"given":"Veerle","family":"Timmermans","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,17]]},"reference":[{"key":"1604_CR1","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/978-3-319-13129-0_2","volume-title":"Web and Internet Economics","author":"M Abolhassani","year":"2014","unstructured":"Abolhassani, M., Bateni, M.H., Hajiaghayi, M., Mahini, H., Sawant, A.: Network Cournot competition. 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