The method which will be presented is identified by the catch phrase Game Theory or, time permitting, the Theory of Games of Strategy. If this is your first encounter with that unlikely sequence of nouns, the sole reaction is probably: Why? Well, the idea takes its name from the circumstance that the study of games is a useful and usable starting p

The average so found is called by mathematicians the expected value. It is evident that this is a use of language which requires special care in interpretation. We do not expect the value (in this case 6) to turn up when Blue and Red use the strategies which lead to this box—indeed, the payoff ‘6’ is actually impossible of occurrence in this box—bu

The Theory of Games is a method of analyzing a conflict, according to the following abstraction: The conflict is a situation in which there are two sets of opposing interests; it may be regarded as a game between two players, each of whom represents one set of interests. Each player has a finite set of strategies from which he may, on any given pla

the sensible object of the player is to gain as much from the game as he can, safely, in the face of a skillful opponent who is pursuing an antithetical goal. This is our model of rational behavior. As with all models, the shoe has to be tried on each time an application comes along to see whether the fit is tolerable; but it is well known in the M

Thus we come to believe it is significant. to count the number of sets of opposing interests around the table, rather than the bodies.

The above two cases illustrate a fundamental distinction among games: It is important to know whether or not the sum of the payoffs, counting winnings as positive and losses as negative, to all players is zero. If it is, the game is known as a zero-sum game. If it is not, the game is known (mathematicians are not very imaginative at times) as a non

However, one-person games (including Solitaire) may be regarded as a special kind of two-person game in which you are one of the players and Nature is the other.

Generally, when the larger of the row minima is equal to the smaller of the column maxima, the game is said to have a saddle-point; and the players should stick to the strategies which intersect at the saddle-point. To discover that there is a saddle-point, each player must examine the game both from his own and the enemy’s point of view. He lists

In this chapter we shall describe a method, called the pivot method, which is powerful enough to ferret out all solutions, and which is efficient enough to be practical; that is, it usually reaches the exact solution in a few steps. The method is more complicated—particularly to describe—than the methods discussed earlier, but we believe the carefu