DEFENSE, DETERRENCE, AND
COMPELLENCE:
THREATS, PROMISES, AND
CREDIBILITY
Topics # 14-16
Defense and Deterrence
• Consider two actors with opposed interests regarding some “prize”:
– A: Aggressor (who wants to change the status quo)
– D: Defender/Deterrer (who wants to maintain the status quo)
• A has two choices:
– to attack D, using offensive capability to seize the “prize” (e.g., territory )
belonging to D, or
– to refrain from attacking A.
• If attacked, D has two choices:
– to (try to) defend against the attack, or
– to give in.
• In this highly oversimplified world, there is some balance between A’s
offensive capability and D’s defensive capability which determines the
payoffs in the event of a conflict.
• Since the players make sequential choices with perfect information, it is
best to represent the game in extensive form.
• Suppose that
– the prize is worth 10 (“units of payoff”)
to both A and D,
– D has an effective defense against A,
• i.e., D can prevent A from seizing
the prize, and
– the cost of fighting is 5 to both A and
D.
• Since D’s defense is effective and the
cost (to D) of fighting is less than the
value of the prize (to D),
– D’s dominant strategy is to defend if
attacked, so
– when A “looks ahead and reasons
back,”
– A chooses to refrain from attacking,
• that is, A is deterred from
attacking in the first place.
Note: the payoffs are (A,D)
Defense and
Deterrence:
Scenario 1
• We see that an effective defense is also a
highly effective deterrent.
• Note also that D does not need to make
an explicit deterrent threat,
– since D is just “threatening” to do what it
makes sense for D to do anyway.
– Such a threat is commonly called a
warning.
• An expensive defense system against a
rational opponent A may be highly
valuable to D even (or especially) if it is
never used.
• In contrast, there may be reason to
regret building expensive defenses
against “attacks” by nature (e.g., floods,
hurricanes, earthquakes, etc.) in the
event they are never used.
– Such defenses do not affect the
likelihood that natural “attacks” occur.
Defense and
Deterrence:
Scenario 1 (cont.)
• Now suppose
– the costs of fighting remain the
same to both A and D, but
– D’s defense is ineffective, i.e.,
• D cannot prevent A from
seizing the prize.
• Since D’s defense is ineffective,
– D’s dominant strategy is to give in
if attacked, so
– when A “looks ahead and reasons
back,”
– A chooses to attack.
• Indeed, attacking is A’s dominant
strategy, since A gains even if D
mounts a (futile) defense.
• However, the next scenario shows
that an ineffective defense may still
be a successful deterrent.
Defense and
Deterrence:
Scenario 2
• Now suppose that the cost of fighting
is 15 for both A and D
– and thereby exceed the value of
the prize,
– but D’s defense remains
ineffective.
• Because D’s defense is ineffective,
– D’s dominant strategy is to give in
if attacked, so
– when A “looks ahead and reasons
back”
– A chooses to attack.
• However, attacking is no longer a
dominant strategy for A, because
– A is counting on “rational” D not
mounting a futile defense.
– Unlike Scenario 2, A will not attack
if A expects D to defend.
Defense and
Deterrence:
Scenario 3
• So if D can make a credible
commitment to defend if
attacked,
– even though the defense is ineffective
– A may be deterred from attacking,
– because the cost of fighting (to A)
exceeds the value of the prize (to A).
• Such a credible commitment
requires an explicit deterrent
threat.
• And the nature of D’s threat is
to say, “if you attack, I will do
something it does make sense
for me to do.”
– So this is not merely a warning,
– and it is inherently difficult to make
the threat credible.
Defense and
Deterrence:
Scenario 3 (cont.)
Defense and Deterrence: Scenario 3 (cont.)
• While there is no question
that D has the capability to
carry out this threat,
– there is considerable question
whether D would actually carry
out the threat if attacked,
– because D will pay the cost of
fighting and still lose the prize.
• In light of the discussion on
Bargaining Tactics,
– D might try to “tripwire” its
defense, etc.
• Finally suppose that the cost of fighting is
for 15 for both A and D,
– but D’s defense is once again effective.
• Even though D’s defense is effective,
– D’s dominant strategy is still to give in if
attacked,
– because the cost of fighting (to D) exceeds
the value of the prize (to D), so
– when A “looks ahead and reasons back”
– A chooses to attack.
• But once again attacking is not a dominant
strategy for A.
• But if D can make a credible commitment to
defend if attacked,
– A is once again deterred from attacking,
– because the cost of fighting (to A) exceeds
the value of the prize (to A).
Defense and
Deterrence:
Scenario 4
• Such a credible commitment
requires an explicit deterrent
threat.
• Once again while there is no
question that D has the
capability to carry out the
deterrent threat,
– there is considerable question
whether D will choose to carry out
the threat if attacked,
– because the cost of fighting exceeds
the value of the prize.
• Note that the payoffs to the players
are symmetric in Scenario 4 (unlike 3),
so D is in a somewhat more favorable
bargaining position in Scenario 4 than
3.
Defense and
Deterrence:
Scenario 4 (cont.)
General Observations
• D may be “the bad guys” (e.g., hostage holders, deterring an “attack” by
authorities).
• A may be “the good guys” (e.g., police trying to free the hostages).
• Note that in the preceding scenarios, no fighting actually occurs,
– except possibly in Scenarios 3 and 4, if D actually carries out a
deterrent threat that (evidently) was not credible to A.
– In the real world,
• A and D may misperceive the payoffs as evaluated by the other
party; and
• the costs of fighting are not fixed because if fighting starts an
endurance contest between A and D may result
– Remember the Dollar Auction Game in Topic #2,
• in which both sides may pay costs of fighting that (greatly) exceed
the value of the prize.
General Observations (cont.)
• An even more important consideration is that the immediate
conflict may be embedded in a larger ongoing conflict in
which reputation effects are important,
– which thereby changes the payoffs to the players,
– as reputations are at stake (perhaps especially for D) in
addition to the value of the prize.
• Remember that in Scenarios 3 and 4, D’s deterrent threat was
to use an ultimately ineffective defense that would impose
high costs on A (as well as D).
Deterrent Threats: Pure Punishment
• But D can make deterrent threats based on the capability to destroy
anything that A values.
– As Schelling notes, it is usually much easier and cheaper (especially in
the modern world) to destroy things than to create (or defend) them.
• In a few hours, the 9/11 terrorists
– destroyed things worth about $100 billion (and years to contruct) at a cost of
about $100,000 (? )
– and took about 3,000 lives at a cost of 19 lives.
• What was unusual is that this action was neither
– an attempt to destroy military capability (like the attack on Pearl Harbor), nor
– fulfillment of a specific deterrent (or compellent) threat.
– Of course, nuclear weapons hugely enhance the capacity to destroy.
– Moreover, bombers and missiles allow D to destroy things of great
value to A without D first defeating and destroying B’s military
capability,
• and may allow A to inflict similar damage in retaliation,
• so the destruction may be mutual.
Deterrence: Threats to Punish (cont.)
• It is important to note the concept and reality of deterrence
are not restricted
– to nuclear weapons (“nuclear deterrence”),
– nor even to military capabilities.
• Another arena of social interaction in which the language of
deterrence is commonly used is the criminal justice system,
– where its applicability is not limited to murder and the
death penalty only.
Conditions for Successful Deterrence
• These appear to be the conditions for successful deterrence:
• D must be able to detect the attack or other action against
which the deterrent threat is aimed.
– This is not problematic in deterring military attacks (least of all a
nuclear attack)
– But it is problematic in
• deterring criminal and other socially harmful acts, and
• deterring violations of arms control and similar international agreements.
• D must have a visible and adequate capacity to carry out the
threat,
– and retain this capacity even if A actually attacks,
– that is, A must not be able to carry out a pre-emptive attack that
deprives D of the capacity to punish.
Conditions for Successful Deterrence (cont.)
• D must be perceived by A to be
– willing to carry out the deterrent threat or
– otherwise committed to carrying it out.
• A must make rational calculations about whether to attack or
refrain from attacking.
• The willingness of D to carry out the deterrent threat is usually
the most uncertain condition, because
– carrying out the threat does not (usually) protect or regain the prize, and
– and the punitive consequences are (usually) visited on D as well as A.
• In principle, all that matters is A’s perception of all these
conditions.
– Deterrence can succeed even if D is bluffing with respect to the first three
conditions,
– but D’s actual capabilities and intentions most reliably shape A’s perceptions.
Coercion and Compellence
• Let’s reconsider Scenario 1, in which D has an effective
defense and the cost of fighting is less than the value of the
prize.
– Remember that D’s effective defense was also a successful deterrent
to a possible attack by A.
• However, if A has the capability to impose punishment
(beyond the costs of fighting) on D greater than the value of
the prize,
– A may be able to coerce D into giving up the prize as a result of a
compellent threat, i.e.,
– A can threaten to punish D (almost certainly at some cost to A also) to
an extent that exceeds the value of the prize (to D) in event D does not
give up the prize.
Coercion and Compellence (cont.)
• Given the extensive form to
the right, if A just looks
ahead and reasons back, A
refrains from attacking or
coercing.
• However, if A can somehow
credibly commit to choosing
“Punish” at the final move,
– A can anticipate that that D
will “Give In” rather than
“Resist” at the previous
move, and therefore
– A can win the prize by means
of the compellent threat.
Types of Credible Commitments
• Consider a sequential choice game with perfect information in
which each player makes one move.
– Let’s label the choices each player has simply Left and Right
– In the absence of any communication, P1 looks ahead a reasons back.
– If credible commitment by P2 is possible, what sorts of commitments
may P2 make that may improve the outcome for P2?
• Such a commitments makes a difference only if it commits P2
to a choice that P2 would not otherwise make.
• P2 may make
– an unconditional commitment (to choose Left or to choose Right), or
– a conditional commitment (e.g., if you choose Left, I’ll chose Right)
• In this game, if P1 looks ahead and
reasons back, the outcome is (R,L) =
(+2,-2).
• But if P2 commits to choose R no
matter what, and if this commitment
is credible to P1, P1 will change his
choice to L and the outcome will be
(L,R) = (-2,+2).
• Note that this game is Chicken,
where
– L = swerve, and
– R = straight.
• In absence of P2’s commitment, P1
has a first-mover advantage, which
P2 tries to deprive P1 of by a preemptive commitment to R.
• Note that P2’s commitment, if
credible, will not actually be tested.
Note: payoffs are (P1,P2)
Unconditional
Commitment
• In this game, if P1 looks ahead and
reasons backs, the outcome is (R,L) =
(+2,-2).
• But if P2 commits (threatens) to
choose R in the event P1 chooses R,
and if this threat is credible to P1, P1
will change his choice to L and the
outcome will be (L,L)= (-2,+2).
• In this simplified game, this may be
regarded as either:
– a deterrent threat (P1 must not
choose R), or
– a compellent threat (P1 must choose
L).
• Note that P2’s threat, if credible, will
not actually be tested,
– So nobody (not even P2) knows for
sure whether P2 would have carried
out the threat.
Conditional
Commitment: The
Threat
• In this game, if P1 looks ahead and
reasons backs, the outcome is (R,R)
= (+2,+2).
• But if P2 commits (promises) to
choose L in the event that P1
chooses L, and if this promise is
credible to P1, P1 will change his
choice to L and, if P2 does not
renege on his promise, the
outcome will be (L,L) = (+3,+3), an
improvement for both players.
• Note that this game is the
Prisoner’s Dilemma, where
– L is “stay silent” and
– R is “confess.”
• Note that P2’s promise, if credible,
will be tested, and P2 will have the
opportunity to renege on the
promise.
Conditional
Commitment: The
Promise
• In this game, if P1 looks ahead and
reasons backs, the outcome is (R,L)
= (+2,-2).
• If P1 wants to improve the outcome
for himself by credible commitment, P1 must make both a threat
and a promise, i.e.,
– if you choose R, I’ll choose R (to
punish you), but
– if you choose L, I’ll choose L also
(and I won’t exploit you by
choosing R).
• If the combined threat and promise
are credible, the outcome will be
(L,L) = (+1, +2).
• Note that P2’s threat, if credible,
will not actually be tested, but P2’s
promise will be tested, and P2 will
have the opportunity to renege on
the promise.
Conditional
Commitment:
Combined Threat
and Promise
Credibility and Risk
• In these example, we have assumed that commitments,
including threats and promises, are either credible or not
credible.
• P1 might instead believe there is some quantitative
probability p (less than 1 but greater than 0) that P2 will live
up to his commitments.
• We can then calculate the critical risk p* that will just suffice
to deter (etc.) P1.
– This critical risk will dependent of the cardinal/interval values of the
relevant payoffs.
Deterrence and Compellence
in a Hostage-Holding Game
• Terrorists, criminals, etc., hold one or more hostages, and they
want to
– avoid capture by the authorities and/or
– coerce the authorities into other concessions.
• They are surrounded by police authorities.
– The authorities want to free the hostages and capture the hostageholders without making any substantial concessions to them.
• The bargaining power of the hostage-holders lies entirely in
the fact they hold the hostages and can harm/kill them.
– If the authorities can somehow free the hostages,
– or if the hostage-holders ever carry out their threat to kill the
hostages,
– the bargaining power of the hostage-holders evaporates and they can
be readily captured.
Hostage-Holding Game (cont.)
• The hostage-holders can use their bargaining power to
support both a deterrent threat and a compellent threat.
– The deterrent threat is: if you (authorities) try to free the
hostages and/or capture us, we will kill the hostages
before you can do so.
– The compellent threat is: if you do not give in to our
demands (for exit from the country, for release our
comrades in prison, for ransom, etc), we will kill the
hostages.
– Carrying out either type of threat is a total defeat for the
hostage-holders (and a substantial -- but not total -- defeat
for the authorities), and therefore
• their threats are not highly credible.
Deterrent vs. Compellent Threats
• Adding to the tension, the authorities have a incentive to
launch a pre-emptive attack to free the hostages and capture
the hostage-holders,
– Before the hostage-holder can carry out their threat,
– and the hostage-holders know the authorities have this incentive
• In such situations,
– the deterrent threat is usually successful (at least for a while) while
– the compellent threat usually fails.
• There are several reasons why (in the real world) compellent
threats are less likely to be successful than deterrent threats.
– But these difference do not show up in simple game representations
of conflict situations.
Deterrent vs. Compellent Threats (cont.)
• With respect to the hostage-holders’ deterrent threat,
– the authorities have the “last clear chance” to avoid mutual disaster
• i.e., initiating a shoot-out that puts the hostages and others at risk,
and
– they almost always are willing to out-wait hostage-holders
• unless the condition of the hostages becomes dire.
• With respect to the hostage-holder’s compellent threat,
– the problem for the hostage-holders is that they must set a deadline
by which time authorities must comply with their demand,
– so in this respect the hostage-holders have the “last clear chance” to
avoid mutual disaster,
• e.g., killing the hostages, and
– they always will be tempted to extend the deadline, and
– the authorities know this.
Deterrent vs. Compellent Threats (cont.)
• There is a second reason why in general deterrence is more
likely to succeed than compellence.
• Real world games do not have complete information, in that
– the players do know each other’s payoffs for sure
– In fact, players may not know all of their their own
preferences for sure.
• This means it is often not clear whether deterrence is needed
in the first place, e.g.,
– whether A will really attack D if A believes they can “get
away with it.”
• Therefore, in the real world
successful deterrence is
often “observationally
equivalent” to unnecessary
deterrence.
– “May This House Be Safe from
Tigers” story [NY Times
Square]
vs.
– “May Western Europe Be Save
from Russians” story [Fulda
Gap]
• This fact also suggests there
may be a problem in maintaining political support for
deterrence over the long
term.
Deterrent
Threats (cont.)
Deterrence vs. Compellence
• Giving in to a deterrent threat
– does not require any change in behavior by A and
– may therefore be invisible and not costly in terms of A’s prestige and
reputation.
– “We were never planning to attack in the first place.”
• On the other hand, giving in to a compellent threat
– does require a change in behavior by the recipient of the threat and
– is therefore highly visible and costly in terms of prestige and reputation.
• (First) Gulf War:
– Iraq-Kuwait pre-August 1990: US deterrence failure
– Iraq-Kuwait post-August 1990: compellence failure (followed by US offensive
success)
• Korea pre/post June 1950 somewhat similar:
– US/Western initial deterrence failure
• Did China try to deter US/UN from crossing the 38th Parallel and “liberating” North
Korea?
• Or did it want a surprise offense to destroy US military capability and prestige?
Deterrent Threats (cont.)
• There is another political problem in maintaining deterrent
threats:
– while successful deterrence is largely invisible (because it
cannot be distinguished from unnecessary deterrence),
– unsuccessful deterrence is highly visible.
• The “Warden’s Survey” of death row inmates.
– His sample is biased, including only deterrence failures.
– The deterrence successes are all outside the prison
• and therefore are not included in the survey
– The deterrence successes outside the prison are mixed in
with
• a vastly larger number of cases of unnecessary deterrence, and
• a some additional cases of deterrence failure.
Generalized Deterrence
• Recall that any immediate conflict may be embedded in a
larger ongoing conflict,
– in which reputation effects are important,
– which thereby changes the payoffs to the players,
– as reputations are at stake in addition to the value of the prize.
• This means that D may have an incentive to defend (or
punish), even if doing so is more costly in the short run than
giving in (and losing the prize).
• Of course, A may likewise may have an incentive to commit
aggression, even if doing so is more costly than refraining
from attack (and not winning the prize).
• Thus early contests of will take on unusual importance,
– e.g., negotiations about the shape of the negotiating table.
Generalized Deterrence (cont.)
• The value of the prize in early contests is not its intrinsic
“strategic value” but its significance as a precedent and an
index of resolve.
– Even if Kuwait produced only “carrots” and the US and others were interested
only in oil, they should still have responded to the Iraqi invasion of Kuwait
(because UAE, Saudi Arabia, etc., produce oil).
– Cf. the domino theory (with reference to Southeast Asia and elsewhere),
– which really came to pass in Eastern Europe in the Fall of 1989.
• Generalized deterrence (“containment”) was especially
important to the U.S. and the West (and to a lesser extent to
the S.U. and the East) during the extended conflict of the Cold
War.
– The Soviet’s major deterrence problems probably lay in Eastern Europe,
– just as Russia’s deterrence problems today probably lie mainly in small
“national” insurgencies (Chechnya, etc.).
• Suppose D has made a commitment to defend some prize
against A,
– e.g., Quemoy/Matsu islands in the
Taiwan Strait but adjacent to the Chinese
mainland.
• Can D “decommit” without
undermining its future credibility?
– “This precedent should not be
interpreted as a precedent.”
– US might hope that an earthquake,
tsunami, typhoon, etc., sinks the islands.
• “Giving in” to Nature does not imply
you will “give in” to adversaries
players.
– D can (try) to redefine the commitment,
• e.g., from Western rights throughout
Berlin to Western rule in West Berlin.
The Art of
Decommitment