1. Decisions and Games. Human life is an unbroken
sequence of decisions made by the conscious individual.
He is continuously confronted with the need for mak-
ing choices, some of them of narrow, others of very
wide scope. In some cases he commands much infor-
mation about consequences of a particular choice, in
most he is quite uncertain. Some affect the immediate
present, others commit him for a distant future. Some
decisions are entirely his own—whether to have an-
other cup of tea, to go for a walk; some involve other
persons—whether to marry X. Many decisions are
made with respect to nature: what planting to choose,
what weather to expect. Many decisions are made by
groups of individuals, and the group decision can be
arrived at by a great variety of processes.
Some decisions arise from a logical structure as in
law. There are also mathematical and logical decisions;
whether π is a transcendental number, or whether to
accept a particular proof of the existence of God. Even
in mathematics there may be uncertainty, as Gödel has
shown.
Decisions must also be made when an individual
plays a game. (First, however, he must make the deci-
sion to play, which is normally though not necessarily
a voluntary one.) In playing the game, the individual
follows rules which, together with the decisions made,
usually determine the winner. In all cases the desire
for optimality (maximum rewards) will arise since
clearly a decision is a choice among alternatives and
the “best” decision will be preferred over all others.
Many different kinds of decisions occur in connection
with games of various types, the number of different
games being indeterminate since always new games
can be invented. In order to describe the behavior of
individuals and to evaluate their choices, criteria have
to be known or must be established.
Clearly a comprehensive theory of decision-making
would encompass virtually all of voluntary human
activity and as such would be an absurd undertaking,
given the infinity of human situations. A more reasona-
ble approach is to develop a science, or sciences, deal-
ing with the principles, so as to govern decision-making
in well-defined settings. In what follows the structure
of that theory will be laid bare as far as this is possible
without going into the use of the underlying mathe-
matics.
Game theory represents a rigorous, mathematical
approach towards providing concepts and methods for
making reasonable decisions in a great variety of
human situations. Thus decision theory becomes part
of game theory. The basic features of the theory are
described in Section 7, below.
