Preliminary Results from Game Theory

A two person zero-sum game is defined as a 3-tuple (X, Y, M) where X and Y are sets and M is real valued function defined on the Cartesian product X × Y. The set X is called the set of admissible pure strategies of player 1 and set Y is called the set of admissible pure strategies of player 2. The function M is called the payoff function of player 1. Player 1 chooses a strategy x of the set X while player 2 chooses a strategy y of the set Y. The choices are done simultaneously and independently and the chosen x and y determine the playoff M (x, y) to player 1 and -M(x, y) to player 2. So, it is considered as if each player hands his choice to a referee who then announces (x, y) and executes the payoffs). In zero-sum game the players have antagonistic interests. The payoffs can be considered as amounts of money or utilities. The data of the game (X, Y, M) are known to both players.