Optimal Control of Disarmament Using the Emigration Level
| Date | 01 June 1983 |
| DOI | 10.1177/002234338302000205 |
| Published date | 01 June 1983 |
| Author | Mark Reitman |
| Subject Matter | Articles |
Optimal
Control
of
Disarmament
Using
the
Emigration
Level*
MARK
REITMAN
The
importance
of
the
emigration
level
as
a
key
control
variable
for
the
disarmament
process
is
discussed
and
confirmed.
The
mathematical
formulation
of
the
optimal
control
of
disarmament
leads
to
the
problem
of
the
optimal
time
control
for
a
system
described
by
the
two
Richardson
linear differential
equations.
The
problem
is
readily
resolved
by
means
of
the
Pontriagin
maximum
principle.
An
illustrative
example
is
presented
which
clearly
shows
that
arms
levels
cannot
be
used
as
control
variables;
this
explains
the
permanent
failure
of
talks
on
the
reduction
of
arms.
Moreover,
it
shows
where
to
look
for
ways
of
actual
peace
strengthening
based
on
disarmament.
I .
Introduction
Peace
between
small
and
large
nations
is
defended
now
by
the
balance
of
deterrence.
But
this
balance
is
by
no
means
stable;
it
can
be
torpedoed
by
any
random
circumstances
(in-
cluding
the
’effect
of
a
dropped
cigarette
on
the
button’).
Politicians
do
their
best
to
agree
on
reducing
the
arms
level,
but
usually
they
fail
to
agree.
However,
they
go
on
hoping
that
the
next
attempt
to
agree
about
this
reduction
will
be
successful;
this
delusion
is
dangerous.
The
scientific
approach
shows
that
these
failures
are
not
occasional:
they
are
rooted
in
the
initial
presumptions
and
are
clearly
observed
from
the
viewpoint
of
current
mathematical
methods.
The
contemporary
theory
of
conflict
between
a
pair
of
countries
is
based
on
the
Richardson
equations
(Richardson
1960)
describing
the
state
of
political
conflict
between
two
countries.
Later
these
equations
were
used
many
times
with
different
interpretations
of
the
coefficients.
Sometimes
additional
terms
were
introduced
(Abelson
1963)
or
the
simulation
process
was
constructed
(Lambelet
1975).
Incidentally,
simulation
processes
were
discussed
sometimes
independently
from
the
Richardson
equations
*
The
Editor
wishes
to
emphasize
that
this
contribution
is
published
in
the
Journal
of
Peace
Research
not
primarily
because
the
paper’s
main
thesis
is
beyond
criticism,
which
we
do
not
think
it is,
but
because
we
want
to
promote
the
dialogue
between
scholars
across
political
and
ideological
boundaries.
We
found
Dr.
Reitman’s
contribution
in
that
sense
highly
inter-
esting
and
worth
publishing.
(see,
for
instance,
Guseinov
et
al.
(1976)
on
the
simulation
of
Greek
ancient
wars).
The
survey
of
Western
studies
in
this
field
can
be
found
in
the
publications
of Ruloff
(1976)
and
Saaty
(1968).
The
latter
was
the
pioneering
publication
in
which
the
application
of
the
optimal
control
was
discussed
and
the
international
conflict
situation
was
represented
by
a
differential
game.
Since
then,
many
writers
have
underlined
the
importance
of
active
steps
in
changing
the
atmosphere
of
fear.
The
most
conspicuous
warning
has
been
made,
perhaps,
by
Boulding
(1976):
’Umbrella
and
raincoat
are
perfect
examples
of
wholly
defensive
weapons
which
diminish
the
impact
of
bad
weather
but
do
nothing
either
to
produce
it
or
to
make
it
cease.
In
the
international
system,
however,
our
nuclear
umbrella
and
our
organization
of
defence
actually
increase
the
probability
that
the
bad
weather
of
war
will
occur.’
In
this
respect,
the
main
aim
of
the
paper
is
rather
the
improvement
of
the
weather
than
the
repair
of
the
umbrella.
Moreover,
the
slight
modification
of
the
Richardson
equations
and
the
application
of
the
optimal
control
theory
show
why
the
attempts
to
curb
the
arms
race
directly
have
failed.
The
optimal
control
cannot
be
applied
directly
to
arms
reduction,
but
it
can
be
inserted
indirectly
by
using
other
control
variables.
If
a
driver
wants
to
increase
the
speed
of
his
non-automatic
car,
say,
from
30
to
40
mph,
he
can
use
the
gear
shift
and
accelerator;
he
will
not
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