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

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 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.

The average so found is called by mathematicians the expected value. It is evident that this is a use of language which requires special care in interpretation. We do not expect the value (in this case 6) to turn up when Blue and Red use the strategies which lead to this box—indeed, the payoff ‘6’ is actually impossible of occurrence in this box—bu

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

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?

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

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.

VALUE

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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