This paper serves as a description of the findings of nuclear
games exercises to test the stability outcomes of deploying defense
systems in a proliferated environment in which seven players
(nations) have nuclear weapons. These games were conducted at
The Heritage Foundation from November 2004 until January 2005,
and involved a wide range of policy experts.
The reasoning behind using games and game theory is based
on the fact that they are, and have been, an important tool used to
analyze the dynamics of war and peace. The security environment in
Asia was used as a model to conduct this Nuclear Game.
The outcomes of our exercises suggest that the presence of
defenses in a multi-player setting not only does not feed
instability, but also may contribute to stability.
- First, the outcome of the games generally showed that the more
widespread the presence of defenses, the lower was the propensity
to ready offensive (nuclear) arms and fire shots with these arms.
It also showed a greater propensity to abandon offensive arms
(disarm) as defenses became more widespread.
- Second, the more widespread the presence of defenses,
the lower the propensity to adopt hostile attitudes toward one
another or move to threaten each other.
- Third, the more widespread the defenses, the less likely an
aggressive actor's conclusions favored aggressive actions.
During the Cold War, the use of game
theory led many scholars to the counterintuitive conclusion that
the best means for avoiding nuclear war was to make both sides--in
this case the United States and the Soviet Union--as vulnerable as
possible to nuclear war's devastating effects. Today, the United
States finds itself in a fundamentally different security
environment. The proliferation of nuclear weapons and the means to
deliver them has resulted in the U.S. facing not only one opponent
of roughly equivalent strength, but potentially multiple
opponents of varying strengths.
Game practitioners and game theorists
have recognized that the characteristics of games with more
than two players are different from those of two-player games.
Chief among these is the presence of the coalition dynamic. As a
result, The Heritage Foundation was determined to explore whether
games or game theory applications to a nuclear proliferated
environment would reveal if the presence of missile defenses does
or does not contribute to nuclear instability in a multi-player
setting, despite earlier determinations by some that they were
destabilizing in a two-player setting.
Thus, the game design attempts to
approximate a multi-player nuclear environment that the U.S. may
face in the future, particularly in regional settings.
In a gaming exercise four iterations
are played, each assuming a different defensive force posture. The
offensive nuclear force postures remained constant. The
defensive force postures ranged from no defensive presence to the
possibility of defenses becoming available to all the players.
The hypothesis this game exercise tested is that a balance of
offensive and defensive forces is not a counterproductive force
posture for the purpose of maintaining stability because it will
not increase strike incentives, particularly with nuclear
weapons, in a multi-player setting. Inherent in this
hypothesis is the view that a multi-player environment is both
so complex and so fluid that the risks associated with a posture of
mutual vulnerability among all the players derived from an
offense-dominant posture--in this case, in a seven-player
setting--are intolerably high.
Therefore, this hypothesis rejects the proposition that all
multi-player settings can be reduced through carefully chosen
assumptions to two-player dynamics and stability outcomes
calculated on the basis of the least stable two-player
relationship. Game-based stability calculations in a multi-player
environment must account for managing stability through times of
potentially dramatic and unpredictable changes in coalitions
among the players. These calculations cannot be based simply on set
coalitions in the context of a discrete confrontation.
A New Game Design
The game is a seven-player, non-zero sum game. It assumes player
rationality, but allows different goals for each of the seven
players. The setting is analogous to a situation in which several
states join the nuclear club.
The Players. The players correspond to nation-states in a
regionally focused geographic setting. The game design uses
abstract descriptions of these players (states) to allow the
individuals playing the game a wider range of options than a strict
adherence to the detailed characteristics of these states
would allow. Nevertheless, the region corresponds roughly to East
The descriptions of both the capabilities and the security
policy preferences of the players (beyond the basic goals of
avoiding a situation in which they are "wounded" or "killed") are
- Player A is a lesser power. In the context of the game,
he has an offensive capacity equivalent to a 15-shot automatic
weapon. Not favoring the status quo, Player A is prepared to
undertake aggression against Player B if given the
opportunity. He also maintains a hostile policy toward Player
G because of Player G's alliance relationship with Player B.
Further, Player A has a high tolerance for risk and is prepared to
consider aggression even if the likelihood of a high payoff is
remote or prospects of losing the game (by being "killed") are
significant. In part, this is because continuation of the status
quo poses a significant risk of regime collapse due to
internal economic and political weaknesses. Player A's
security goals, starting with the most immediate and ending
with the most ambitious, are: 1) regime survival; 2) forcing Player
G to withdraw from the region, thus breaking his alliance
relationship with Player B; 3) hegemonic power over Player B; and
4) the conquest of Player B. Player A is roughly equivalent to
- Player B is also a lesser power. He is allied with a
major power (Player G). However, unlike player A, he prefers the
status quo and is not likely to use force unless provoked.
Likewise, he is a power with a low tolerance for risk. In fact, he
is seeking ways to avoid confrontations with Player A. His security
goals, starting with the most immediate, are: 1) deterring or, if
necessary, defending against an attack by Player A; 2)
settlement of the dispute with Player A and the establishment of a
stable relationship; and 3) continuation of the alliance with
Player G, at least until the dispute with Player A is settled.
Player B is roughly equivalent to South Korea.
- Player C is the third lesser power in the game. While an
independent power, he has a relatively close relationship with
Player A and shades his position in favor of Player A in
confrontations with Players B and G. This shading is in part a
response to a view that Player G's involvement in Player C's region
is a meddlesome presence. Like Player A, Player C is not a
status quo power and will assert his position. He also has a
high tolerance for risk. Player C's security goals, starting with
the most immediate, are: 1) lessening the likelihood of a
military conflict between Player A and Player B; 2)
facilitating the withdrawal of Player G from the region; 3)
regional hegemony; and 4) the conquest of Player E. Player C
is roughly equivalent to the People's Republic of
- Player D is the fourth lesser power in the game. While
now an independent power, Player D formerly had an alliance
relationship with Player G and maintains a friendly relationship
with Player G. While Player D, at the outset of the game, is
neutral regarding any possible confrontation between Player A
and Player C on one side, and Players B and G on the other, he is
likely to side with Players B and G if pressed. Like Player B,
Player D is a status quo power and has a low tolerance for
risk. He is not aggressive and seeks to avoid confrontation. His
security goals, starting with the most immediate, are: 1) to avoid
getting drawn into a military conflict, particularly as a means for
avoiding attacks by either Player A or Player C; 2) a continued
presence in the region by Player G; 3) nuclear
disarmament by Players A and B; and 4) blocking regional
hegemony by Player C. Player D is roughly equivalent to
- Player E is the final lesser power in the game. At the
outset of the game, Player E is neutral regarding any confrontation
between Player A and Player C on the one hand, and Player B and
Player G on the other. Nevertheless, he historically has had a
tense relationship with Player C. If drawn into the conflict,
Player E is likely to side with Players B and G. Player E also is a
status quo power and has a low tolerance for risk.
Player E's security goals, starting with the most immediate, are:
1) deterring or, if necessary, defending against an attack by
Player C; 2) continuing the presence in the region by Player
G; and 3) blocking regional hegemony by Player C. Player E is
roughly equivalent to Taiwan.
- Player F is the first of two major military powers
in the game. In the context of the game, he has an offensive
capability that is equivalent to a 200-shot chain gun. However,
Player F's gun is not well maintained and has a propensity to
malfunction. This limits the probability of a high payoff if he
uses his weapon. Regarding any confrontation between Players A and
C and Players B and G, Player F is strictly neutral. In part, this
is because he sees few vital interests at stake in such a
confrontation. This same view leads Player F, at least in this
instance, to view the status quo with satisfaction and to
possess a relatively low tolerance for risk. Player F's
primary security goals are: 1) to lessen the likelihood
of a conflict between Players A and C and Players B and G; and 2)
to avoid being drawn into such conflict, particularly if being
drawn in could lead to a direct confrontation with either Player C
or Player G. Player F is roughly equivalent to
- Player G is the final player in the game. He is also the
second of two major powers in the game, with an offensive
capability equivalent to a 200-shot chain gun. Unlike Player F,
however, his weapon is well maintained. In later iterations of
the game, in order to test the hypothesis that defenses are
not destabilizing in multi-player games, Player G will be provided
access to a defensive capability in the form of a bulletproof
vest. He will have the option to furnish this capability to other
players as well as himself. As indicated earlier, he is allied
with Player B and, as a result, is subject to threats from Player
A. As a major power, Player G prefers the status quo and has
a low tolerance for risk. He is unlikely to resort to force unless
provoked. On the other hand, he will seek a way to come to the
defense of his ally, Player B, unless the risks of losing (being
"killed") are quite high or the payoff for victory is exceedingly
low. Player G's security goals, starting with the most
immediate, are: 1) preventing a nuclear attack on his
territory; 2) preventing an attack by Player A, particularly in
collusion with Player C, on Player B; 3) nuclear disarmament by
Players A and B in particular, and perhaps by others; and 4)
continuation of his strong presence in the region. Player G is
roughly equivalent to the United States.
The game works in the following way. It is divided into
"moves" (decisions made by each player at one point in time) and
"rounds" (the compilation of the decisions made by all the players
at the same point in time). The game requires each player to make
moves within each round by reviewing his options on two
levels--attitudes and force postures.
Player Attitudes. The first level is the diplomatic
level. Here, each player assesses the relationship he would like to
have with each of the other players. They are categorized as: 1)
hostile; 2) unfriendly; 3) neutral; 4) friendly; and (5)
Force Postures. The second level of options pertains
to force postures and is also reviewed in every round. Five of the
players, A through E, have a holstered automatic weapon, such
as an Uzi (15-shot). The remaining two players (Players F and G)
have chain guns (200 shots). These weapons correspond to
nuclear-armed ballistic missiles. These offensive armament levels
are held constant throughout the game in order to test the
hypothesis in terms of various levels and configurations of
Any player can voluntarily disarm ("quit"), but the gameis not
designed as an arms control exercise. Any player can draw his
weapon at any time ("ready"), which is necessary for him to shoot.
Any player can put his readied weapon back into the holster
("holster"). Any readied weapon can be aimed at another player
("threaten"). Any player can fire a readied weapon at another
player ("attack"). Any player can choose to hide his weapon hand
with a shroud held by his off-hand ("shroud"), which precludes
other players from knowing whether his weapon is ready. A decision
either to threaten or to attack another player results in the
lifting of the shroud, which may not be restored until after the
relevant player holsters his weapon.
Player G can put on a bullet-proof vest in two turns, which
reduces the number of penetrating shots from the other players.
This limited defense takes the form of "defensive interceptors."
Thus, it is neither a perfect defense nor capable of rebuffing
All players start out holstered, unshrouded, undefended, and
Attack Outcomes. the game defines three possible
outcomes for a player who is attacked: (1) "functional," which
is the initial status for all players; (2) "wounded"; and (3)
"killed." The requirements to wound or kill are preset for each
player and vary from player to player.
Communications. Private communications and public
announcements among the players are used to augment the game
structure. Private communications are limited. Each player is
allowed to initiate one such communication between any two rounds
(although it may be directed at more than one player) and to
respond to any private communication directed at him, but only
The Game Manager. Finally, a game manager supervises the
conduct of the game. The game manager is empowered to disallow a
player's move on two grounds. The first ground is that the move is
inconsistent with the description of the player that was provided.
The second is that the move is disruptive to the testing of
Results of the 2004-2005 Game
To test the hypothesis that defenses will not contribute to
instability in a proliferated setting, four iterations of the game
were played. Each corresponded to a different defensive
posture, in which offensive forces were held constant through all
Game Iteration #1: Multilateral
Mutually Assured Destruction. The first iteration of the
game has Player G opt not to put on the vest (furnish himself
with defensive interceptors), despite the fact that he has the
ability to do so. This decision also leads him to decide not
to furnish the vest (defensive interceptors) to any other player.
This policy is applied in a setting in which there are two obvious
sources of confrontation--Player A's desire for the conquest of
Player B and Player C's desire for the conquest of Player E--and
the potential for a variety of less obvious confrontations.
All of these sources of confrontation are of interest to Player G
because of his deep involvement in the region as a global power.
Inherent in this policy choice is the belief that the Cold War
policy of relying exclusively on offensive forces to maintain
security is the best approach, even in a proliferated
General Observations. A shooting war ended the first
iteration of the game and revealed that, at least in an environment
in which no defenses are permitted, the inherent instabilities
are quite serious. It is important to draw some specific
conclusions from the first iteration of the game.
- Failing to account for multiple axes of possible confrontation
and conflict is a serious mistake.
- Distinguishing between players that are aggressive,
non-status quo powers and those that are not aggressive and
in favor of the status quo is a key to maintaining
- Crossing the nuclear threshold carries serious incentives for
- Players can be expected to mix their choices between deterrence
and deception, with varying impacts on stability.
- The coalition dynamic is both complex and immensely important
Game Iteration #2: Lesser Power
Vulnerability. In the second iteration Player G
decides to put on the vest (deploy defensive interceptors), but
adopts a policy that precludes him from furnishing the vest
(defensive interceptors) to any other player.
This policy choice was based on the belief that the best option
for stability was for Player G to focus on defending himself, while
ruling out defenses for other players, because the presence of
defenses in the region would exacerbate the tensions already
present in the region.
General Observations. A shooting war ended the playing of
this second iteration of the game, but it was not encouraged by the
presence of the defenses in the hands of Player G. The results of
the second iteration of the game confirmed the finding of the first
iteration that offensive deterrence is a fragile concept for
stability in this proliferated environment. This combination
of low predictability and high stakes increased the risk that
players would miscalculate and lead to shooting.
The shooting war, which resulted in the deaths of every player
but Player G and the serious wounding of Player G, had two
proximate causes. Both causes were serious miscalculations by
Players A, C, and F under the Red Alliance they formed in the
course of the game.
There is no discernible evidence that Player G's defenses
prompted the two miscalculations by the players of the Red
The history of this iteration of the game drives the observer to
conclude that it is inherently more difficult for a superpower to
maintain the necessary credibility to bolster both deterrence and
stability in this proliferated environment. This speaks to the
issue of the fragility of deterrence that was raised at the outset
of these general observations. A superpower's allies, with
their own nuclear arsenals, are more likely to look to their own
resources to provide for their security. They are also more
likely to look to other outlets--namely, alliances with
nuclear powers other than the superpower--to meet their
security requirements. Adversaries, in turn, are more likely to see
opportunities to divide the superpower from his friends and allies
and pursue these divisive policies aggressively. Unfortunately for
Player G, his credibility problems may have come with the
territory. His defenses did not cause them. In fact, they
contributed to his survival.
Game Iteration #3: Theater-Only Defenses. In the third
iteration of the game Player G adopts a policy of not putting
on the vest (deploying defensive interceptors) except that he
decides to provide the vest (defensive interceptors) to other
players on a case-by-case basis.
This policy choice is based on the belief that the best option
for stability is for Player G to forgo defenses for himself while
providing them to his friends and allies on the basis that fielding
such defenses for himself would upset the strategic balance
with Player F and jeopardize arms control initiatives between
General Observations. The third iteration of the game
revealed that in this proliferated setting, with defenses available
to select players other than Player G, the potential for
instability was significant; however, it was possible for the
players to overcome this potential for instability. A shooting war
was avoided in this instance. What was necessary to overcome these
sources of instability was for the players to find buffers that
increased the predictability of their behavior and lessened the
stakes resulting from swings in coalitions.
The presence of defenses in the hands of select players other
than Player G did not contribute to a circumstance in which a
conflict became imminent or make it more difficult to achieve the
stable outcome. In fact, the evidence suggests that the
defenses served as a source of buffers needed to avoid an
exchange of shots.
While it would be wrong to suggest that the presence of
defenses in the hands of select lesser powers was the only factor
in generating this outcome, specific observations suggest that
the defenses made a significant contribution.
- The ability of Player G to offer defenses to his friends and
allies provided another means to bolster their confidence in him
and limit opportunities by the aggressive powers to split
Player G from his friends and allies.
- The presence of defenses in the hands of the non-aggressive
powers lessened their reliance on offensive threats to pursue
their security interests.
- The presence of defenses bolstered the deterrence
capabilities of the non-aggressive powers by raising questions in
the minds of the aggressive powers about the potential
ineffectiveness of preemptive strikes.
- The presence of the defenses served to create a barrier against
an aggressive nuclear alliance that included Player F.
- Player G's ability to confer defenses gave him an additional
tool for inducing disarmament by other players.
Game Iteration #4: Global
Offense-Defense Mix. In this case, Player G decides to put
on the vest (deploy defensive interceptors) and provide it
(defensive interceptors) to other players on a selective
This policy choice was based on the belief that the best option
for stability is for Player G to see the proliferation threat as a
global problem that requires a concerted defensive effort that
serves to protect Player G and others on equivalent terms.
General Observations. The fourth iteration of the game
revealed that while the potential for instability remained
high, it could be overcome. Again, no shooting war resulted. The
coalition dynamic remained unpredictable and carried extremely high
stakes for the players. This combination of low predictability
and high stakes carried the risk that the players would
The question regarding the hypothesis was whether the presence
of defenses in the hands of Player G and select other players
hindered attempts to moderate tensions or undermined the steady
progress made throughout the game toward select disarmament and a
stable outcome. The answer was no. In fact, the evidence suggests
that the opposite was true. Defenses served as a source of buffers,
which were necessary to avoid either preemptive attacks or
At the surface level, the evidence suggested that, in this
iteration of the game (as with the third iteration), this was
the case because no shots were fired and no players were wounded or
killed. Additional evidence to bolster this view resulted from the
fact that at no point in this game did a player lodge a direct
threat against another player and an exchange of shots was never
more than unlikely. Several observations indicate why the presence
of defenses certainly did not undermine, and may have
contributed to, this positive outcome.
- As with the third iteration of the game, Player G's ability to
offer defenses to his friends and allies served to bolster their
confidence in him and to reduce the likelihood that they would act
- Player G was able to use the offer of defenses to temper the
aggressive tendencies of players hostile to him.
- The presence of defenses in the hands of both aggressive and
non-aggressive powers lessened their reliance on offensive threats
to pursue their security interests.
- Player G's policy of providing defenses to himself as well
as to others lessened the incentive for aggressive powers to
threaten him as a source of political leverage.
- The presence of the defenses undermined Player F's effort to
form an alliance with Player C.
- Player G's ability to confer defenses induced disarmament in a
way that allowed a brief examination of the dynamic present in a
circumstance of selective proliferation.
Comparing the Four
Comprehensive analysis requires comparing the outcome of each
iteration with the outcomes of the other three. The following
analysis reinforces the observations following each iteration of
the game that the presence of defenses, far from inducing
instability, actually appears to contribute to a stable
Force Posture Considerations. From the viewpoint of
comparing stability outcomes in the four iterations in regard to
the players' force postures, it is appropriate to examine three
criteria. The first criterion is the propensity of the players
to ready their offensive weapons, with a move to ready
representing a step toward instability. The second criterion
is the propensity of the players to disarm, with a move to disarm
representing a step toward stability. The final criterion is the
propensity of the players to strike. This is the most relevant
criterion because the propensity to strike is tantamount to the
definition of instability.
Comparing the four iterations of the game in light of these
three criteria results in three observations:
Observation 1: The more widespread the
defenses, the lower the propensity of players to ready their
The offensive readiness levels trend down across the four
iterations. Generally speaking, there is a positive correlation
between the incremental addition of defenses and the reduction
in the players' propensity to ready their offensive weapons.
Therefore, to the extent that lowered readiness postures
contribute to stability, defenses may have played a contributing
role in generating a stable outcome.
Observation 2: The more widespread the
defenses, the higher the propensity of players to disarm.
Likewise, there was a positive correlation between the
incremental increase in the presence of defenses and the propensity
to disarm when all four iterations of the game are considered.
Therefore, to the extent that selective disarmament contributes to
stability, it is fair to conclude that the presence of defenses may
have contributed to stability.
Observation 3: The more widespread the
defenses, the lower the propensity of players to strike.
When the analysis of the propensity to strike extends across all
four iterations of the game, it is clear that the broadening
presence of defenses corresponds to a lower propensity to
strike on the part of all players. This is the most important
criterion regarding the impact on stability brought about by the
presence of defenses. The positive correlation between the
increased presence of defenses and the players' lower propensity to
strike suggests that the defenses contributed to stability.
Two criteria are most applicable in assessing the factors for
stability or instability in the game in the area of player
relations. The first is the propensity of the players to adopt
hostile attitudes toward one another. The second is the propensity
of the players to threaten others, specifically with an offensive
strike. Comparing the four iterations of the game in light of these
two criteria results in two observations.
Observation 1: The more widespread the
defenses, the lower the number of times that players adopted
hostile attitudes toward one another.
In the first iteration of the game, with no defenses
present, hostile attitudes held by one player toward another
fluctuated between two and four throughout the game. The second
iteration of the game, which allowed only Player G to field
defenses, saw hostile attitudes range between five and six in
each round until after Round 7. Thereafter, they escalated rapidly
and peaked at 19. The third iteration of the game, with
defenses in the hands of select players other than Player G, saw
hostile attitudes dip from six following Round 1 to three at
the beginning of Round 5. In the final iteration of the game, in
which Player G fielded defenses and provided them to other
players, the only hostile attitudes that persisted throughout
the game were between Player C and Player E.
These observations reveal an anomaly between the first and
second iterations of the game as appeared in the observations
stemming from the relevant force postures. It is important to keep
in mind, however, that the game manager terminated the game in the
first iteration in a circumstance when additional hostile attitudes
were likely to emerge in subsequent rounds. Further, the conflict
that occurred in the second iteration of the game resulted from
factors that had nothing to do with the presence of defenses.
Nevertheless, when the observations are collected from all four
iterations of the game, they show a positive correlation between
the presence of defenses and relatively low numbers of hostile
attitudes demonstrated by the players. This serves to bolster
the argument that defenses may have contributed to stability in
this proliferated setting.
Observation 2: The more widespread the
defenses, the lower the number of times that players threatened one
Not surprisingly, these observations track closely with those
made regarding hostile attitudes. The anomaly between the first and
second iteration persists for reasons that do not involve
Player G's possession of defenses. The comparison of all four
iterations of the game shows a trend toward fewer threats as
defenses are added. This positive correlation again suggests
that the presence of the defenses contributed to stability.
This technical study suggests that President George W. Bush
acted just in time when he decided in 2001 to accelerate the
missile defense program and jettison the 1972 Anti-Ballistic
Missile (ABM) Treaty and its underlying concept of mutually assured
destruction (MAD). The results of playing the game indicate that
multilateralizing MAD would have been a bad choice for stability.
Further, the results suggest that President Bush was right in
adopting a global approach to missile defense that brings the
friends and allies of the U.S. into the program while extending the
defense to U.S. territory. This is preferable to fielding
defenses exclusively for U.S. territories or limiting the
defense to theater settings.
This study also suggests that President Bush and the Department
of Defense's 2002 Nuclear Posture Review were right in pointing to
the need for a responsive nuclear infrastructure. The
unpredictable nature of the proliferated environment makes
this necessary. It is all but certain that such an environment
will result in the need for new nuclear weapons to meet new
military requirements. While there is a range of options for the
proper mix of offensive and defensive forces, it is clear that the
U.S. nuclear deterrent remains essential to maintaining peace
and stability. Defenses cannot and should not become a substitute
for offensive nuclear forces.
The proliferated setting assumed by the game presents the U.S.
with sobering problems. The risks of a highly destructive conflict
are significant. The President and Congress must address these
problems, if for no other reason than because it presents an
opportunity to prevent this proliferated environment from
becoming a reality.
The good news is that President Bush and Congress, by
opting for a policy that advances the U.S. toward a mix of
offensive and defensive forces, have put the nation's defense
posture on the right path. With determination, the United States
can address the threat posed by nuclear proliferation and start
taking steps to reverse a disturbing trend. The next step is to
undertake aggressive nuclear weapons and missile development and
deployment programs that match the policy direction that has been
established over the past four years.
Baker Spring is
F.M. Kirby Research Fellow in National Security Policy at The
Heritage Foundation. This paper is a summary of his book,
Nuclear Games: An Exercise Examining Stability and Defense in a
Proliferated World. These remarks were delivered at the United
States Army War College.