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Matrix games with fuzzy payoffs have spread itself nowadays in diverse fields. Fuzzy game theory with triangular type-1 fuzzy numbers are visited more by researchers. In this paper, we consider matrix games with payoffs as triangular type-2 intuitionistic fuzzy numbers, i.e., Triangular Type-2 Intuitionistic Fuzzy Matrix Game (TT2IFMG) as a new and rare concept. A new ranking function is used to get relevant solutions of TT2IFMG. We are living in times of unprecedented scientific-technical advancement, yet facing several critical global problems that threaten human welfare and our ecosystem. Water management, a burning problem of the Earth now-a-days, is treated here under the scanner of TT2IFMG environment where we discuss some policy-management toward the free and fair accession of water against its limited resources.