This paper is devoted to formulating the concept of a symmetric bimatrix game and to developing results analogous to those for symmetric matrix games. We show that, given any bimatrix game or two-person non-zero- sum game, there exist two equivalent symmetric games, with the property that symmetric equilibrium strategies for the symmetrized games yield equilibrium strategies for the original game. An adaptation of Nash's proof of the existence of equilibrium strategies for any bimatrix game is used to show that any symmetric bimatrix game with entries which are real numbers does admit of a symmetric equilibrium point. Finally, the question of whether this result on the existence of symmetric strategies holds if the matrices and strategy vectors are in an arbitrary ordered field is answered in the affirmative through the use of a metamathematical argument. The argument is sufficiently general to encompass many other results in game theory.
By: J. H. Griesmer; A. J. Hoffman; A. Robinson
Published in: RC959 in 1963
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