Abstract

In the theory of games developed by John v. Neumann [1], [2] the normalized form of a zero sum two person game is defined as follows (see section 14.1 in [2]): There are two players and there is a function K(ri, T2) of two variables mr and T2 given where Ti and T2 can take only a finite number of values. Player 1 chooses a value 1ri and player 2 chooses a value T2, each choice being made in complete ignorance of the other, and then players 1 and 2 get the amounts K(ri, T2) and -K(-ri, T2), respectively. Obviously, player 1 wishes to maximize K(ri, TO) and player 2 wishes to minimize K(Ti, T2). As v. Neumann has shown (see section 14.5 in [2]), the choice of ri by player 1 and the choice of T2 by player 2 can be rationalized if the game is strictly determined, i.e., if