WHAT IS GAME THEORY?
A two person game is any competition or conflict between two opponents, called players. It is a zero-sum game if what one player loses, the other gains. A payoff matrix for a two person zero-sum game denotes the gains and losses to player 1 called the row player.
BEST PURE STRATEGY FOR A ROW PLAYER IN A FINITE ZERO 2-SUM GAME:
Determine the least element in each row of the payoff matrix and choose the row where the least element is the largest - max(min).
BEST PURE STRATEGY FOR A COLUMN PLAYER IN A FINITE ZERO 2-SUM GAME:
Determine the largest element in each column of the payoff matrix and choose the column where the largest element is the smallest - min(max).
An element of a payoff matrix that is simultaneously the max(min) and min(max) is an equilibrium point and the number is the value of the game. Every finite game has a Nash equilibrium.