This paper deals with two-person non-zero sum games with interval pay-offs. An analytic method for solving such games is given. A pair of Nash Equilibrium is found by using the method. The analytic method is effective to find at least one Nash Equilibrium (N.E) for two-person bimatrix games. Therefore, the analytic method for two-person bimatrix games is adapted to interval bimatrix games.
The purpose of this paper is to determine when and under which conditions the solution and game value of the infinite interval matrix games will exist. Firstly, the concept of a reasonable solution defined in interval matrix games was extended to infinite interval matrix games. Then, the solution and game value were characterized by using sequences of interval numbers defined by Chiao ["Fundamental Properties of Interval Vector Max-Norm", Tamsui Oxf J Math Sci, 18(2): 219-233, 2002.] and their concept of convergence of interval numbers. Considering that each row or column of the payoff matrix is a sequence of interval numbers, we assume that each row converges to the same interval number 𝛼 ̃= [𝛼 𝑙 , 𝛼 𝑟 ] and each column to the same interval number 𝛽 ̃= [𝛽 𝑙 , 𝛽 𝑟 ]. In a conclusion, the existence of the solution of 𝐺 ̃ is shown.
This paper deals with two-person non-zero sum games with interval payoffs. Graphical method to find a mixed strategy equilibrium is adapted to interval bimatrix games.In addition, interval bimatrix games Nash equilibrium is attained by graphical method. Numerical examples are also illustrated.
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