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In a game problem, when the situation is formulated as the gain of one equals the loss of other, the game is called zero-sum. But actually, one player's win is not always the other's loss. Such a game is referred to as non-zero sum or bimatrix game. The work provided in this research is primarily elaborated on linguistic bimatrix games under 2-tuple linguistic environment. This class of bimatrix games consists of payoffs having entries as linguistic 2-tuples, that are based on a finite subscript-symmetric additive linguistic set defined in the domain, where  g  is a positive integer. In this direction, a novel linguistic equilibrium concept is defined to solve such games, and a methodology based on a nonlinear linguistic programme is proposed to compute mixed Nash equilibrium. The proposed methodology is sufficient to evaluate the Nash equilibrium and the maximum expected payoffs corresponding to each player simultaneously in a single programme. The necessary and sufficient conditions for the existence of Nash equilibrium and a computation procedure are also provided. Finally, some hypothetical working examples are given to show the practical applicability of the defined methodology. The proposed methodology is also applied to solve two-player constant sum linguistic games.

A methodology for solving bimatrix games under 2-tuple linguistic environment