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 zero-sum games the payoffs represent strictly an exchange of assets; one player wins the quantity that the other loses. We have compromised this principle somewhat in games played against Nature (used as examples here and there), where we have computed strategies for the personal player as if he were playing against an opponent who shared his va

This is one of the fundamental distinctions in Game Theory, namely, the number of persons—distinct sets of interests—that are present in the game. The form of analysis and the entire character of the situation depend on this number. There are three values, for the number of persons, which have special significance: one, two, and more-than-two.

We believe it possible that Game Theory, as it develops—or something like it—may become an important concept and force in many phases of life.

You will recall: we require that the scheme for our game be reduced to a payoff matrix—a rectangular array (possibly square) of numbers, indexed against the various strategies which are available to the players.

One should always look first for a saddle-point; the process is painless and concludes the work if there is one. Recall that we inspect each row to find its minimum, select the greatest of these, and then inspect the columns to find the maxima, selecting the least of these. If the two numbers (called, incidentally, the maxmin and minmax) are equal,

We have indicated that the number of persons involved is one of the important criteria for classifying and studying games, ‘person’ meaning a distinct set of interests. Another criterion has to do with the payoff: What happens at the end of the game?

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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