8. Applications. Application is the final test of
theories but may be hard to come by. Decision theory
and game theory have a potentially wide range of uses.
Those already made are limited partly because of the
newness of the field, because of computational difficul-
ties, and partly because the theories are in a state of
active development which produces new concepts and
theorems. The distance in time and difficulty from an
abstract theory to application is always large when a
fundamentally novel development occurs. This period
may stretch over generations. Some directions of ap-
plication are becoming clear, however. Decision theory
is basic for, and indeed inseparable from, modern sta-
tistics. The use of the minimax theorem has given rise
to a new turn in that science (primarily due to A. Wald)
and produced a large literature. Noteworthy is a study
by J. Milnor (1954) on games against nature in which
various possible criteria, due certain authors such as
Laplace, A. Wald, L. J. Savage, and L. Hurwicz, were
investigated regarding their compatibility. Milnor
showed that no criteria satisfy all of a reasonable set
of axioms and it is an open problem whether new ideas
can be evolved to resolve this impasse. Since this is
a game against nature, then our incomplete and
changing knowledge of nature's laws also has to be
taken into account—a further complication not spe-
cifically considered by Milnor or others. Nature may
be infinitely complex and therefore can never be
“found out” completely.
Game theory has a profound bearing on economics.
Many special problems have been attacked such as
oligopoly (markets with few sellers) which could never
be adequately treated by conventional methods. Par-
ticularly noteworthy is the work by Shapley and Shubik
(1965 to date). The penetration to other areas such as
bargaining, auctions, bidding processes, general equi-
librium, etc., is slow but steady. The very structure
of existing theory is threatened once it is recognized
that there is no determinism and that no one, not even
the state, controls all variables, as was explained above.
But recognition of this indeterminism demands the
scrapping of more than can be immediately replaced,
and this causes a profoundly disturbing situation: one
shows the logical inadequacy of existing theories but
cannot offer a specific immediate and detailed replace-
ment. Also recall that false theories often have had
significant workability (Ptolemy) and therefore, though
doomed, could live together with their ultimate re-
placement (Copernicus) for a considerable time.
Sociology, with a less advanced theory than eco-
nomics will undoubtedly become a fertile field for
applications once the connections are seen. In particu-
lar the distinction between the rules of games and the
standards of behavior (which depend on previously
formulated rules but are the consequences rather than
antecedents of games) offer wide areas for sociological
investigations.
In political science there are increasingly many ap-
plications. Going back to Condorcet's voting paradox
(1785), which is the possibility of an inconsistent col-
lective choice, even when individual choices are con-
sistent, great strides have been made in illuminating
voting procedures (Farquharson, 1969), many of these
steps resting on the theory of weighted majority games.
In addition political power play, with favors granted,
side payments made, bluffs, promises kept and broken,
is as ideal and fetile a field for the new concepts as
one could wish, but the path is thorny, especially
because of the preliminary, difficult quantification of
matters such as “political advantage” and the like. Of
particular significance is the illumination of the bar-
gaining and negotiation process. A considerable litera-
ture has emerged which is of great practical value
though it is highly technical. One question, for exam-
ple, is how the contracting parties should deal with
disclosure of their own utility functions in the process
of negotiating. Another is the proof, given by von
Neumann and Morgenstern (1944), that of two bar-
gaining parties the one will get the upper hand which
has the finer utility scale, a better discernment of ad-
vantages. Negotiation is always possible except when
there is full antagonism, which exists only in a zero-sum
two person game. In all other cases negotiations are
possible, whether the game be zero-sum or not.
The application to military matters is obvious and
some possibilities have been explored extensively in
many countries. The idea of a “strategy” has after all
since ancient times been embedded in military activi-
ties, but it is noteworthy that the modern theory did
not take its inspiration from the military field but from
social games as a far more general and fruitful area
from which it could radiate.
Combat and conflict, however, are as deeply rooted
in human nature as is cooperation, so that the combi-
nation of both, emerging with singular clarity in
military affairs, makes this field naturally attractive for
study. As a consequence there is now a game theoretic
literature concerning combat, deployment, attrition,
deterrence, pursuit, and the like. Also the insight that
in war—especially in nuclear war—both parties may
lose (“Pyrrhic victories”) has found precision in the
formulation of games with negative payoffs to all. In
most cases it is only in the 1960's that all these notions
have become precise and were in part successfully
applied in a concrete and computational form.
Game theory has also been used in ethics, biology,
physics, and even engineering. This spread of appli-
cations is two-fold. First, in ethics the problems of
decision-making are essential, and it may appear that
they consist primarily in imposing constraints on the
individual or on society (Braithwaite, 1955). This view
would exclude technically feasible strategies for moral
reasons (though permitted within the rules of the
game). This exclusion of strategies shows how ethical
decisions involve other persons, positively or nega-
tively, directly or indirectly, singly or in groups, as well
as compromises and commitment. An ethics that con-
siders only a normative system of possible ideals (which
can never be fully explicit in view of the infinity of
situations that may be encountered), or single decisions
by single, isolated individuals is unable to deal with
crucial issues of that field. The mere exclusion of a
feasible strategy on moral grounds implies that the
consequences of its use are known and can be disap-
proved. But the consequences depend also on the strat-
egies chosen by the others and prediction of this type
may be impossible. The moral code may forbid murder
but accept killing on command in war, and then try
to qualify what kind of commands are valid and which
are not. This goes clearly beyond the mere establish-
ment of an abstract normative system, not considered
in action. Analysis taking into account the above points
leads to a probabilistic ethics if only because the not
strictly determined games demand the use of mixed
strategies. These ideas are now only in the first state
of development. They are fundamentally different from
previous abortive applications of mathematics to eth-
ics, such as by Spinoza.
Second, in the other areas game theory appears as
a mathematical technique rather than as a model.
Certain processes, say in engineering, can be inter-
preted as if they were games because of a formal
correspondence. This then makes the use of the exten-
sive mathematical apparatus of game theory possible.
Illustrations would necessarily be of a rather special-
ized character and are therefore omitted here, though
the large field of linear programming with its many
variants (of great practical importance) must be men-
tioned. Game theory and programming theory are
closely related by virtue of the well known duality
theorem for linear programming.
Biologists (Lewontin, 1961; Slobodkin, 1964) have
interpreted evolution in game theoretic terms, in spite
of the difficulty for a nonteleological biology to use
the purposeful orientation of game theory. By means
of appropriate reinterpretation, including that of util-
ity, it is shown that game theory can give answers to
problems of evolution not provided for by the theory
of population genetics. It is possible to identify an
optimal strategy for survival of populations in dif-
ferent environments.
Some of these developments involve game theory
strictly as a technology (not as a model) and in some
it is still doubtful whether a true model character can
be accepted (as possibly in biology). There are here
transitional phases of high interest and it is impossible
to foresee the development of these tendencies.
