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

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

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 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?

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

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.

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 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

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?

Game Theory is very similar in spirit to the Theory of Gravitation. Both attempt to treat broad classes of events according to abstract models. Neither tries to model all the complexities present in any situation.