Studies of the bi-matrix game are mostly based on the assumption that all players are rational people. But research results are conflict with the realities. In this paper, putting emotional factors in game structure, in non-expected utility theory, we established RDEU-Bimatrix Game Model which containing players' emotional preference. Using the Brouwer fixed-point theorem proved the existence of Nash equilibrium in RDEU-Bimatrix Game Model. Finally, through the numerical analysis we discussed the influence of players' emotional preference for Nash equilibrium.
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