The　aim　of　this　paper　is　to　develop　a　methodology　for　solving　matrix　games　with　payoffs　of　trapezoidal　intuitionistic　fuzzy　numbers　(TrIFNs).　In　this　methodology,　the　concepts　of　TrIFNs　and　solutions　for　matrix　games　with　payoffs　of　TrIFNs　are　defined.　Two　new　auxiliary　intuitionistic　fuzzy　nonlinear　programming　models　are　hereby　constructed　to　solve　matrix　games　with　payoffs　of　TrIFNs.　Using　a　new　ranking　method　based　on　the　value　and　ambiguity　of　TrIFNs,　the　auxiliary　intuitionistic　fuzzy　nonlinear　programming　models　are　transformed　into　the　bi-objective　parameterized　nonlinear　programming　models,　which　are　further　integrated　into　the　parameterized　linear　programming　models,　which　are　used　to　obtain　solutions　of　matrix　games　with　payoffs　of　TrIFNs.　The　validity　and　applicability　of　the　proposed　methodology　in　this　paper　are　illustrated　with　a　numerical　example.　©　2014　TFSA.