p.1 The
purpose of this book is to present a discussion of some fundamental questions of economic theory which require
a treatment different from that which they have found thus far in the literature. The analysis is concerned with
some basic problems arising from a study of economic behavior which have been the center of attention of economists for a
long time... Our
considerations will lead to the application of the mathematical
theory of "games of strategy"...
We shall first have to find
in which way this theory of games can be brought into relationship with economic theory, and what their common elements are.
p.4 The reason why mathematics has not been more successful in economics must, consequently, be found elsewhere.
The lack of real success is largely due to a combination of unfavorable circumstances, some of which can be removed gradually.
To begin with, the economic problems were not formulated clearly and are too often stated in such vague terms as to make mathematical
treatment a priori appear hopeless because it is quite uncertain what the problems really are. There is no point
using exact methods where there is no clarity in the concepts and issues to which they are to be applied. Consequently the
initial task is to clarify the knowledge of the matter by further careful descriptive work.
p.4-5 mathematical economics has not achieved very much. The underlying vagueness and ignorance has not
been dispelled by the inadequate and inappropriate use of a powerful instrument that is very difficult to handle.
p.6-7 It is necessary to begin with those problems which are described clearly, even if they should not
be as important from any other point of view... The great progress in every science came when, in the study of problems which
were modest as compared with ultimate aims, methods were developed which could be extended further and further.. It seems
to us that the same standard of modesty should be applied in economics. It is futile to try to explain - and "systematically"
at that - everything economic. The sound procedure is to obtain first utmost precision and mastery in a limited field, and
then to proceed to another, somewhat wider one, and so on.
p.7-8 what is important is the gradual development of a theory, based on a careful analysis of the ... facts.
... Its first applications are necessarily to elementary problems where the result has never been in doubt and no theory is
actually required. At this early stage the application serves to corroborate the theory. The next stage develops when the
theory is applied to somewhat more complicated situations in which it may already lead to a certain extent beyond the obvious
and familiar. Here theory and application corroborate each other mutually. Beyond lies the field of real success: genuine
prediction by theory. It is well known that all mathematized sciences have gone through these successive stages of evolution.
p.11 the others are guided, just as he himself, by rational principles - whatever that may mean - and no
modus procedendi [way of proceeding] can be correct which does not attempt to understand those principles and the
interactions of the conflicting interests of all participants... general theory must cover all these possibilities, all intermediary
stages, and all their combinations.
p.36 Even if one of these is actually applied, i.e. if one particular alliance is actually
formed, the others are present in a "virtual" existence: Although they have not materialized, they have contributed
essentially to shaping and determining the actual reality.
p.44 We repeat most emphatically that our theory is thoroughly static. A dynamic theory would unquestionably
be more complete and therefore preferable. But there is ample evidence from other branches of science that it is
futile to try and build one as long as the static side is not thoroughly understood.
p.45 A static theory deals with equilibria. The essential characteristic of an equilibrium is that
it has no tendency to change, i.e., that it is not conductive to dynamic developments. An analysis of this feature
is, of course, inconceivable without the use of certain rudimentary dynamic concepts. The important point is that they are
rudimentary. In other words: For the real dynamics which investigates the precise motions, usually far away from equilibria,
a much deeper knowledge of these dynamic phenomena is required... A dynamic theory - when one is found - will probably describe
the changes in terms of simpler concepts
p.125 But our proof, which guarantees the validity of one (and only one) of these three alternatives [that
a chess position is either won for white, won for black, or either player can draw], gives no practically usable method to
determine the true one. This relative, human difficulty necessitates the use of those incomplete, heuristic methods
of playing, which constitute "good" Chess
