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

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

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?

PART

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.

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

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

This is an important concept in Game Theory, that of mixed strategies: the concept that a player should sometimes use one pure strategy, sometimes another, and that the decision on each particular play should be governed by a suitable chance device. We can anticipate that this will be a feature of most games, that it will fail to appear only when c

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

A strategy. is a plan so complete that it cannot be upset by enemy action or Nature; for everything that the enemy or Nature may choose to do, together with a set of possible actions for yourself, is just part of the description of the strategy. So the strategy of Game Theory differs in two important respects from the conventional meaning: It must