Of　the　different　types　of　games,　the　matrix　games　with　fuzzy　payoffs　have　been　extensively　discussed.　Two　major　kinds　of　solution　methods　have　been　devised.　One　is　the　defuzzification　approach　based　on　ranking　functions.　Another　is　the　two-level　linear　programming　method　which　can　obtain　membership　functions　of　players＇　fuzzy　values　(or　gain　floor　and　loss　ceiling).　These　methods　cannot　always　ensure　that　players＇　fuzzy/defuzzified　values　have　a　common　value.　The　aim　of　this　paper　is　to　develop　an　effective　methodology　for　solving　matrix　games　with　payoffs　expressed　by　trapezoidal　fuzzy　numbers　(TrFNs).　In　this　methodology,　we　introduce　the　concept　of　Alpha-matrix　games　and　prove　that　players＇　fuzzy　values　are　always　identical,　and　hereby,　any　matrix　game　with　payoffs　expressed　by　TrFNs　has　a　fuzzy　value,　which　is　also　a　TrFN.　The　upper　and　lower　bounds　of　any　Alpha-cut　of　the　fuzzy　value　and　the　players＇　optimal　strategies　are　easily　obtained　through　solving　the　derived　four　linear　programming　problems　with　the　upper　and　lower　bounds　of　Alpha-cuts　of　the　fuzzy　payoffs.　In　particular,　the　fuzzy　value　can　be　explicitly　estimated　through　solving　the　auxiliary　linear　programming　with　data　taken　from　the　1-cut　and　0-cut　of　the　fuzzy　payoffs.　The　proposed　method　in　this　paper　is　illustrated　with　a　real　example　and　compared　with　other　methods　to　show　validity　and　applicability.