The　aim　of　this　paper　is　to　develop　a　bilinear　programming　method　for　solving　bi-matrix　games　in　which　the　payoffs　are　expressed　with　intuitionistic　fuzzy　sets　(IFSs),　which　are　called　IFS　bi-matrix　games　for　short.　In　this　method,　using　the　equivalent　relation　between　IFSs　and　interval-valued　fuzzy　sets　(IVFSs)　and　the　operations　of　IVFSs,　we　propose　a　new　order　relation　of　IFSs　through　introducing　a　ranking　function,　which　is　proven　to　be　a　total　order　relation.　Hereby　we　introduce　the　concepts　of　solutions　of　IFS　bi-matrix　games　and　parametric　bi-matrix　games.　It　is　proven　that　any　IFS　bi-matrix　game　has　at　least　one　satisfying　Nash　equilibrium　solution,　which　is　equivalent　to　the　Nash　equilibrium　solution　of　corresponding　parametric　bi-matrix　game.　The　latter　can　be　obtained　through　solving　the　auxiliary　parametric　bilinear　programming　model.　The　models　and　method　proposed　in　this　paper　are　demonstrated　with　a　real　example　of　the　e-commerce　retailers’　strategy　choice　problem.　©　Springer　Nature　Singapore　Pte　Ltd.　2019.