The　aim　of　this　paper　is　to　develop　a　nonlinear　programming　method　for　computing　the　elements　of　the　interval-valued　cores　of　n-person　cooperative　games　in　which　coalitions’　values　are　expressed　with　intervals,　which　are　often　called　interval-valued　n-person　cooperative　games　for　short.　With　finding　out　the　maximum　satisfactory　degree　in　the　situation　with　the　features　of　inclusion　and/or　overlap　relations　between　intervals,　this　paper　tries　to　explore　the　cooperation　chance　in　this　type　of　cooperative　games.　Firstly,　we　define　the　concept　of　interval-valued　cores　of　interval-valued　n-person　cooperative　games　and　satisfactory　degrees　(or　ranking　indexes)　of　comparing　intervals　with　the　features　of　inclusion　and/or　overlap　relations.　Hereby,　we　propose　the　auxiliary　nonlinear　programming　model　and　method　for　solving　interval-valued　cores　of　any　interval-valued　n-person　cooperative　games.　The　developed　method　can　provide　cooperative　chance　under　the　situation　of　inclusion　and/or　overlap　relations　between　intervals,　while　the　traditional　interval　ranking　method　may　not　assure　that　the　interval-valued　cores　exist.　This　method　is　a　complement　to　the　traditional　methods　rather　than　the　alternative　one.　The　feasibility　and　applicability　of　the　model　and　method　proposed　in　this　paper　are　illustrated　with　a　numerical　example.　©　2016,　Springer-Verlag　Berlin　Heidelberg.