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

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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 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

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

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.

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

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.

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