The　purpose　of　this　paper　is　to　develop　a　methodology　for　solving　a　new　type　of　matrix　games　in　which　payoffs　are　expressed　with　triangular　intuitionistic　fuzzy　numbers　(TIFNs).　In　this　methodology,:　the　concept　of　solutions　for　matrix　games　with　payoffs　of　TIFNs　is　introduced.　A　pair　of　auxiliary　intuitionistic　fuzzy　programming　models　for　players　are　established　to　determine　optimal　strategies　and　the　value　of　the　matrix　game　with　payoffs　of　TIFNs.　Based　on　the　cut　sets　and　ranlcing　order　relations　between　TIFNs,　the　intuitionistic　fuzzy　programming　models　are　transformed　into　linear　programming　models,　which　are　solved　using　the　existing　simplex　method.　Validity　and　applicability　of　the　proposed　methodology　are　illustrated　with　a,　numerical　example　of　the　market　share　problem.