The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy (Dover Books on Mathematics)

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.

A perennial difficulty in modelmaking of the analytical (as opposed to wooden) variety is the illness which might well be known as criterion-trouble. What is the criterion in terms of which the outcome of the game is judged? Or should be judged?

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.

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.

I owe a very special debt to Warren Weaver of the Rockefeller Foundation, who was driven, by friendship and by interest in the topic, to read it very hard. His single-minded insistence on clarity of exposition was always of great value and sometimes a nuisance—especially in instances where his style and skill were better suited than my own to the p

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The contexts of interest to us are those in which people are at cross-purposes: in short, conflict situations.

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