Some Comments on the Meaning and Use of Game Theory
| Published date | 01 March 1968 |
| Date | 01 March 1968 |
| DOI | 10.1177/001083676800300106 |
| Subject Matter | Articles |
Some
Comments
on
the
Meaning
and
Use
of
Game
Theory
Knut
Midgaard
1.
On
the
Concepr
of
Game
Theory
i
The
potential
utility
or
disutility
of
game
theory
for
the
development
of
a
sound
the-
ory
of
strategic
decisions,
and
for
sound
strategic
decision-making,
is
a
question
to
which
prominent
writers
have
taken
an
inquiring
attitude.
One
reason
for
being
open
and
inquiring
on
this
point
is
that
it
is
not
obvious
that
every
competent
person
understands
exactly
the
same
by
the
term
‘game
theory’.
Another,
closely
related
rea-
son
is
that
it is
not
obvious
what
will
grow
out
of
game
theory
as
it
is
known
today.2
2
Primarily,
game
theory
is
a
mathemati-
cal
theory,
with
its
own
vocabulary,
ax-
ioms,
definitions,
classifications,
theorems,
proofs,
and
methods.3
This
formal
theory,
with
its
interpretation
and
with
the
data
it
requires,
does
not
suffice
to
solve
decision
problems
or
account
for
decisions.
In
order
to
make
good
a
decision
a
player
needs
something
more
than
the
’mathematical’
description
of
the
game
in
question
(the
rules
of
the
game
and
the
utility
functions)
and
the
information
to
be
deduced
from
it.
He
may
follow
a
decision-rule
according
to
which
assumptions
about
the
other
players’
structural
knowledge
states,
analytic
states,
and
analytic
knowledge
states
are
irrele-
vant.4
However,
these
aspects
of
the
situa-
tion
are
likely
to
be
taken
into
account,
and
complicated
extra-mathematical
reasonings
incorporating,
among
other
things,
the
re-
sults
of
the
mathematical
deductions,
may
be
required.
In
some
cases
any
reasonable
decision-
maker
will
know
what
to
do
as
soon
as
an
equilibrium
point -
or
an
equilibrium
point
of
a
special
kind -
has
been
found.
To
the
extent
that
these
cases
dominate
our
mental
picture,
the
extra-mathematical
premisses
required
for
a
decision
will
easily
be
ig-
nored.
In
other
cases,
however,
e.g.
where
there
are
two
or
more
non-interchangeable,
jointly
admissible
equilibrium
points,
extra-
mathematical
reasonings
get
into
focus.
To
the
extent
that
such
cases
dominate,
the
de-
scription
and
classification
of
the
extra-
mathematical
reasonings,
and
of
the
entities
and
relations
they
are
linked
to,
are
more
likely
to
be
considered
an
integral
part
of
the
theory
of
games.
Personally,
I
find
that
such
descriptions
and
classifications
must
be
considered
an
integral
part
of
game
theory
if
this
theory
is
to
be
a
decision
theory.
So
I
fmd,
for
in-
stance,
that
Thomas
C.
Schelling’s
account
of
clues
and
focal
points
should
be
consid-
ered
a
central
game-theoretic
contribution.5
I
am
not
certain
that
every
game
theorist
would
agree,
and
I
would
guess
that
those
who
are
of
a
different
opinion,
if
there
are
any,
are
so
mainly
because
they
hesitate
to
recognize
anything
as
a
part
of
game
theory
until
it
has
been
integrated
in
an
axiomatic
theory.
Both
for
this
reason
and
because
the
prob-
lem
is
important
in
itself,
we
have
to
con-
sider
the
question
to
what
extent
proposi-
tions
about
the
dynamics
of
extra-mathe-
matical
reasonings
can
be
integrated
in
a
109
modified
axiomatic
theory.
We
also
have
to
consider
the
utility
of
such
propositions
in
the
cases
where
axiomatization
is
im-
possible.
Let
us
first
look
at
Schelling’s
theory
of
tacit
coordination
on
the
basis
of
strategic
clues.
A
significant
point
here
is
that
stra-
tegic
clues
can
consist
of aspects
of the
plays,
outcomes,
players,
etc.
which
are
not
taken
care
of
by
the,
mathematical
description
of
the
situation.
In
fact,
there
is
no
limit
as
to
what
aspects
can
become
clues,
or
parts
of
clues.
It
may
seem
therefore
as
if
an
axio-
matization
of
tacit
coordination
would
re-
quire
a
drastic
expansion
of
the
vocabulary
and
semantics
of
the
axiomatic
theory,
and
probably
also
of
its
syntax.
In
principle,
the
whole
language
of
the
persons
in
question
would
be
relevant.
Against
this
consideration
two
points
can
be
made.
First,
it is
conceivable
that
two
persons
who
know
that
they
are
likely
to
participate
in
’games’
where
tacit
co-
ordination
will
be
required,
make
a
list
of
potential
clues
which
are
likely
to
occur,
and
work
out
a
rank
ordering
over
these
so
as
to
avoid
a
coordination
problem
of
the
second
order
in
cases
where
more
than
one
potential
clue
obtains.
In
this
way
they
may
elaborate
decision
criteria
which
can
be
integrated
in
an
axiomatic
theory
the
lan-
guage
of
which
is
not
necessarily
very
rich.
Second,
it
is
conceivable
that,
for
certain
classes
of
persons
and
situations,
empirical
research
will
reveal
such
regularities
that
the
emergence
of
strategic
focal
points
can
be
axiomatized
without
any
drastic
expan-
sion
of
the
language
of
the
theory.
Against
the
relevance
of
these
consider-
ations
the
following
points
can
be
made.
Two
persons
who
want
to
work
out
the
kind
of
decision
criteria
outlined
are
not
unlikely
to
find
out
that
it
is
beyond
their
capacity
to
survey
the
possible
situations
so
well
that
they
can
make
a
useful
list
of
po-
tential
clues;
and
in
the
cases
where
deci-
sion
criteria
have
been
worked
out,
these
may
very
well
prove
insufficient.
As
to
em-
pirical
research,
inductions
are
not
unlikely
to
prove
arbitrary
or
irrelevant
because
of
the
complexities
of
real
life
situations.
These
objections
are
an
appeal
to
com-
mon
sense.
Philosophical
argument
may
also
be
presented.
One
might
argue,
for
example,
that
because
of
the
possible
depth
and
uniqueness
of
any
situation
which
in-
volves
some
kind
of
personal
encounter,
it
may
be impossible
to
predict
which
struc-
tural
elements
will
serve
as
a
strategic
clue
in
a
given
situation,
if
there
will
be
any
clue
at
all.
One
might
also
argue
that
man
is
always
transcending
his
past
and
present,
and
therefore
regularities
of
the
past
need
not
obtain
in
the
future.
In
particular,
the
following
case
may
obtain.
A
person
is
going
to
participate
in
a
’game’
where
tacit
bargaining
will
be
required.
From
his
social
science
literature
he
knows
that
a
certain
aspect
of
the
situation
almost
in-
variably
turns
out
to
become
the
strategic
clue
of
that
kind
of
game.
Now,
another
clue
would
be
more
favourable
to
him.
Owing
to
his
knowledge
he
therefore
starts
out
to
consider
whether
he
has
any
chance
of
giving
a
sufficient
salience
to
what
he
wants
to
be
the
clue.
Perhaps
this
is
pos-
sible,
e.g.
by
making
a
choice,
early
in
the
game,
which he
would
not
have
considered
if
he
had
not
been
aware
of
the
results
of
empirical
research
on
games.
To
the
extent
that
axiomatization
of
the
process
of
tacit
coordination
is
impossible,
one
is
left
with
general
statements
like
the
following:
a
play
or
a
strategy
combination
is
likely
to
become
the
strategic
focal
point
of
the
game
if
it
is
jointly
known
or
as-
sumed
to
stand
out
through
some
unique
and
salient
feature.
What
is
the
value
of
such
propositions ?
I
submit
the
following
answer.
They
can
help
an
observer
of
a
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