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The Cuban Missile Crisis: The great Game Theory paradox.
Collin Costello
Bradford Area High School
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Abstract
Game Theory provides evidence in the support of the United States in the widely
disputed outcome of the Cuban Missile Crisis. It is evident that through precise moves, the
United States played a dominant move over the Soviets in the battle for the title of the most
powerful Nuclear Country. The origins of the game’s validity have been disputed due to poor
moves the Soviets played in which caused a (3, 0) outcome of the Cuban Missile Crisis. If the
Soviet Union had not wavered from their demand that the United States removed their nuclear
missiles out of Turkey for them (the Soviet Union), to take their missiles out of Cuba, the game
would have resulted in a (2,2) tie, where both countries would have benefited.
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The Cuban Missile Crisis: The great Game Theory paradox
"The Cuban Missile Crisis stands as a seminal event. History offers no parallel to those
thirteen days of October 1962, when the United States and the Soviet Union paused at the
nuclear precipice. Never before had there been such a high probability that so many lives would
end suddenly." (Essence of Decisions, 1971). The Cold War, specifically the Cuban Missile
Crisis was an extremely tense time for the American population. In addition to being tense, it
was also a breakthrough period in Game Theory. An applied mathematics, Game Theory studies
situations in which there are several stakeholders, who all have different goals, as well as whose
actions affect the outcome and the other players. Game Theory proves that the Cuban Missile
Crisis was favorable for the United States of America.
As events transpired in the modern world, it is to apply game theory mathematics to
analyze possible outcomes. It is always relevant to research Game Theory and specific events in
which large breakthroughs show all sides of a problem; the moves each side takes; and the
actions or reactions the initial move causes. Game Theory is, without a doubt, one of the most
important strategical theories of the modern age.
It is evident that the model of the Cuban Missile Crisis presents is a paradox. When
Game Theorists analyze the Cuban Missile Crisis, they conclude the fact that it should have
ended much differently. When It is easier to foresee mass war and retaliation against an act of
war dealing with nuclear arms than it is to see a cooperative (whether forced or not) end to the
problem. The Cuban Missile Crisis is theoretically incorrect. The events that transpired during
those frightful October days do not seem to coincide to present day analyses of how they should
have went. Cuba, feeling oppressed by the United States of America should not have backed
down, nor Russia, anger rising cooperated. While the United States “played their cards right”, in
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essence, only portraying a small amount of knowledge of the crisis, the events that occurred still
do not hold true to the strategic model that Game Theory derives.
The models of Game Theory are derived from many different places. When one first
models a problem they model the moves a player can make and label them, for example, 0,
which equals the least-favorable outcome; 1, which is somewhat not favorable; 2, which is
somewhat favorable; and 3, which is the most desired. Game Theory states that is understood
that the two players are sane in nature, concerning making decisions and acting rationally in their
game. As seen to the right, Game Theory Analyses are
portrayed in a table fashion with the player one of the left,
player two on the top (Duffy). The game on the side is the
“Prisoners Dilemma,” the oldest, most known Game Theory
model.
The Prisoners Dilemma is a game which involves two
prisoners who were accused of a crime, and also were the only witnesses of the crime. To be
convicted, the prisoners had to testify against each other. If neither testified against the other,
they would both be released. In the model above, 0 is life in prison; 1 is representing a shorter
jail time; 2 represents neither of them going to prison, and 3 represents when one prisoner tricks
the other to not testify against him, claiming he wouldn’t testify against the other. This action
would make the game a (2,2) but then does testify, making it a (3,0) game in the player that
testifies favor (Duffy).
Game Theory analyzes events like the Cuban Missile Crisis, because it is able to factor in
all of the elements at stake (Brans). The Cuban Missile Crisis was one of the most tense
moments in United States history. The Cuban Missile Crisis transpired from the 16th of October,
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in1962 until the 28th of that same month and year. In the history of the United States, nothing is
analogous to the dissonance felt between the United States and Russia, who were both ready to
fire nuclear warheads at one another. For thirteen days, the two governments stood at the brink of
war. The tension between the two countries was caused due to numerous reasons including the
Arms Race and the Castro Regime (Allison, 1971).
The escalation of the tension between Russia and the United States corresponded directly
to the development of nuclear capability. As the two countries continuously developed stronger
warheads, the tension to not fall behind escalated (Robert). During his Presidential Campaign,
John F. Kennedy repeatedly spoke of a "missile gap" between the United States and the Soviet
Union. Soon to President, John F. Kennedy had different information. After he was elected,
President Kennedy still claimed to his story that the Soviets had more missiles than the United
States, however; Soviet Chairman, Khrushchev, was aware that there was no missile gap
(Library).
Chairmen Khrushchev decided to test President Kennedy. He began pressuring Berlin to
become a Communist country. In addition, Khrushchev instructed his army to build a wall
surrounding West Berlin. President Kennedy, responded by stating that there was no missile gap.
The United States had more missiles than Soviet and was not afraid to release them. Chairman
Khrushchev now felt pressured to act. He knew that the United States missiles could reach the
entirety of his land and also knew that the Soviets missile could not respond if there was an
attack (Library).
This knowledge led Chairmen Khrushchev to the aid of the Cubans. On December 19,
1960, Cuba openly admitted its allegiance with the Soviet Union. Responding to this, Kennedy
terminated all diplomatic relation with Cuba. In addition, he also pledged to not intervene
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militarily to overthrow the Castro government. However, Kennedy backed a group of Cuban
exiles who would later invade Cuba at the Bay of Pigs in a mission to spark to an Anti-Castro
revolution. Chairman Castro’s forces however ceased more than a thousand of the Castro
Rebellion force, in turn making the Bay of Pigs invasion a failure. After uncovering and stopping
President Kennedy's plan, Castro announced that Cuba would be receiving Soviet aid which
would make any attack on the Cubans, by the United States, an act of World War.
While at a summit with Soviet Chairmen Khrushchev, the CIA director John McCone
sent President Kennedy a memo expressing his belief that the Soviets deployed Medium-Range
ballistic missiles (nuclear warheads) to Cuba. Responding to this knowledge, Kennedy orders a
U-2 (reconnaissance plane) flight over Cuba, which uncovered multiple missile sights in Western
Cuba. Based on the information the Reconnaissance Mission uncovered, Kennedy formed a
group called "Ex-COMM", which would help him discuss possible diplomatic or military actions
to respond to the situation in Cuba.
Kennedy's Ex-COMM group decided on two different options: 1. A missile strike,
demolishing the launch sites as well as the warheads, 2. A blockade on Cuba. The Joint Chiefs of
Staff, along with the Air Force strongly urged President Kennedy towards an Air Strike. While at
a meeting with Andrei Gromyko, a Statesman and spokesperson for Russia, President Kennedy
was informed that the measures by the Soviets, protecting the Cubans were just that, simply to
help defend the Cubans from an attack on the United States. Knowing better than to trust this
information, Kennedy moved quickly forming a decision on how to act. Ruling that an air strike
may not destroy all missile heads in Cuba, President Kennedy chose a blockade, but called it a
"defensive quarantine" because the word "blockade" is considered to be an "act of war" in the
military community.
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On October 22rd, 1962, President Kennedy addressed the nation, stating:
"Good evening my fellow citizens:
This Government, as promised, has maintained the closest surveillance of the Soviet
military buildup on the island of Cuba. Within the past week, unmistakable evidence
has established the fact that a series of offensive missile sites is now in preparation
on that imprisoned island. The purpose of these bases can be none other than to
provide a nuclear strike capability against the Western Hemisphere.
Upon receiving the first preliminary hard information of this nature last Tuesday
morning at 9A.M., I directed that our surveillance be stepped up. And having now
confirmed and completed our evaluation of the evidence and our decision on a
course of action, this Government feels obliged to report this new crisis to you in
fullest detail.
The characteristics of these new missile sites indicate two distinct types of
installations. Several of them include medium range ballistic missiles, capable of
carrying a nuclear warhead for a distance of more than 1,000 nautical miles. Each of
these missiles, in short, is capable of striking Washington, D. C., the Panama Canal,
Cape Canaveral, Mexico City, or any other city in the southeastern part of the United
States, in Central America, or in the Caribbean area….”
President Kennedy, in these first three paragraphs, set the stage for what he knew would be
a very tense period in the United States. He presented information to the nation about the
“offensive missile sites” in which the Soviet Union had installed in Cuba. These first three
paragraphs introduce the country to the most stressful events of modern history. President
Kennedy give details about the missile sites and how the Soviet Union, with these
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installations, could effectively hit every major city in the western hemisphere. President
Kennedy made a bold move by accusing the Soviet Union of installing troops in Cuba, not
for their protection, yet, for his own.
“…Acting, therefore, in the defense of our own security and of the entire Western
Hemisphere, and under the authority entrusted to me by the Constitution as endorsed
by the Resolution of the Congress, I have directed that the following initial steps be
taken immediately:
First: To halt this offensive buildup, a strict quarantine on all offensive military
equipment under shipment to Cuba is being initiated. All ships of any kind bound for
Cuba from whatever nation or port will, if found to contain cargoes of offensive
weapons, be turned back. This quarantine will be extended, if needed, to other types
of cargo and carriers. We are not at this time, however, denying the necessities of life
as the Soviets attempted to do in their Berlin blockade of 1948.
Second: I have directed the continued and increased close surveillance of Cuba and
its military buildup. The foreign ministers of the OAS, In their communiqué' of
October 6, rejected secrecy on such matters in this hemisphere. Should these
offensive military preparations continue, thus increasing the threat to the hemisphere,
further action will be justified. I have directed the Armed Forces to prepare for any
eventualities; and I trust that in the interest of both the Cuban people and the Soviet
technicians at the sites, the hazards to all concerned of continuing this threat will be
recognized.
Third: It shall be the policy of this Nation to regard any nuclear missile launched
from Cuba against any nation in the Western Hemisphere as an attack by the Soviet
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Union on the United States, requiring a full retaliatory response upon the Soviet
Union.
Fourth: As a necessary military precaution, I have reinforced our base at
Guantanamo, evacuated today the dependents of our personnel there, and ordered
additional military units to be on a standby alert basis.
Fifth: We are calling tonight for an immediate meeting of the Organ of Consultation
under the Organization of American States, to consider this threat to hemispheric
security and to invoke articles 6 and 8 of the Rio Treaty in support of all necessary
action. The United Nations Charter allows for regional security arrangements-and the
nations of this hemisphere decided long ago against the military presence of outside
powers. Our other allies around the world have also been alerted.
Sixth: Under the Charter of the United Nations, we are asking tonight that an
emergency meeting of the Security Council be convoked without delay to take action
against this latest Soviet threat to world peace. Our resolution will call for the prompt
dismantling and withdrawal of all offensive weapons in Cuba, under the supervision
of U.N. observers, before the quarantine can be lifted.
Seventh and finally: I call upon Chairman Khrushchev to halt and eliminate this
clandestine, reckless, and provocative threat to world peace and to stable relations
between our two nations. I call upon him further to abandon this course of world
domination, and to join in an historic effort to end the perilous arms race and to
transform the history of man. He has an opportunity now to move the world back
from the abyss of destruction-by returning to his government's own words that it had
no need to station missiles outside its own territory, and withdrawing these weapons
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from Cuba-by refraining from any action which will widen or deepen the present
crisis-and then by participating in a search for peaceful and permanent solutions.
This Nation is prepared to present its case against the Soviet threat to peace, and our
own proposals for a peaceful world, at any time and in any forum-in the OAS, in the
United Nations, or in any other meeting that could be useful-without limiting our
freedom of action. We have in the past made strenuous efforts to limit the spread of
nuclear weapons. We have proposed the elimination of all arms and military bases in
a fair and effective disarmament treaty. We are prepared to discuss new proposals for
the removal of tensions on both sides—including the possibilities of a genuinely
independent Cuba, free to determine its own destiny. We have no wish to war with
the Soviet Union—for we are a peaceful people who desire to live in peace with all
other peoples.
But it is difficult to settle or even discuss these problems in an atmosphere of
intimidation. That is why this latest Soviet threat—or any other threat which is made
either independently or in response to our actions this week—must and will be met
with determination. Any hostile move anywhere in the world against the safety and
freedom of peoples to whom we are committed—including in particular the brave
people of West Berlin—will be met by whatever action is needed.
Finally, I want to say a few words to the captive people of Cuba, to whom this
speech is being directly carried by special radio facilities. I speak to you as a friend,
as one who knows of your deep attachment to your fatherland, as one who shares
your aspirations for liberty and justice for all. And I have watched and the American
people have watched with deep sorrow how your nationalist revolution was
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betrayed-and how your fatherland fell under foreign domination. Now your leaders
are no longer Cuban leaders inspired by Cuban ideals. They are puppets and agents
of an international conspiracy which has turned Cuba against your friends and
neighbors in the Americas-and turned it into the first Latin American country to
become a target for nuclear war—the first Latin American country to have these
weapons on its soil.
These new weapons are not in your interest. They contribute nothing to your peace
and well-being. They can only undermine it. But this country has no wish to cause
you to suffer or to impose any system upon you. We know that your lives and land
are being used as pawns by those who deny your freedom. Many times in the past,
the Cuban people have risen to throw out tyrants who destroyed their liberty. And I
have no doubt that most Cubans today look forward to the time when they will be
truly free-free from foreign domination, free to choose their own leaders, free to
select their own system, free to own their own land, free to speak and write and
worship without fear or degradation. And then shall Cuba be welcomed back to the
society of free nations and to the associations of this hemisphere.
My fellow citizens: let no one doubt that this is a difficult and dangerous effort on
which we have set out. No one can foresee precisely what course it will take or what
costs or casualties will be incurred. Many months of sacrifice and self-discipline lie
ahead—months in which both our patience and our will will be tested—months in
which many threats and denunciations will keep us aware of our dangers. But the
greatest danger of all would be to do nothing.
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The path we have chosen for the present is full of hazards, as all paths are—but it is
the one most consistent with our character and courage as a nation and our
commitments around the world. The cost of freedom is always high-but Americans
have always paid it. And one path we shall never choose, and that is the path of
surrender or submission.
Our goal is not the victory of might, but the vindication of right-not peace at the
expense of freedom, but both peace and freedom, here in this hemisphere, and, we
hope, around the world. God willing, that goal will be achieved.
Thank you and good night." (Library of JFK)
In this segment of his speech, President Kennedy outlay’s a seven step plan to end the
Cuban Missile Crisis. He outline that a strict quarantine on all offensive military equipment be
originated. He promised more in-depth and comprehensive surveillance of Cuba. He stated that
any missile launched on the Western Hemisphere would be seen as an attack on the United
States. He organized meetings and called upon Chairman Khrushchev to halt his surreptitious,
irresponsible threat to world peace.
After Kennedy’s speech, the U.S.’s military’s defensive raised to DEFCON 2, the highest
level of security in United States history (The Cuban Missile Crisis and Game Theory). After
being approved by the OAS (Organization of American States), including all North and South
American states, Kennedy ordered navy ships to quarantine an 800 mile radius around Cuba. At
the same time, President Kennedy sent his brother, Robert, to the Soviet Embassy for a meeting
with Ambassador Dobrynin who delivered a letter to the President from Chairman Khrushchev
stating that the actions taken by the United States are “serious threats to peace and security of
peoples” (The Cuban Missile Crisis and Game Theory). President Kennedy, giving Khrushchev
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space, lowered the quarantine to a 500 mile radius. The quarantine sent all but one Soviet ship
away from Cuba.
On 26th, 1962, Khrushchev sent a letter to Kennedy proposing the removal of Soviet
missiles if Kennedy would publicly declare never to invade Cuba. President Kennedy sends word
the next day that the United States would not invade Cuba if Khrushchev removes Soviet
missiles from their shores. On October 28th, in 1962, Chairman Khrushchev announced over the
radio that the Soviet Union would be pulling their missiles off of the island of Cuba, thus ending
the Cuban Missile Crisis. However Chairman Khrushchev’s actions, based on game theory
evidence, do not make sense.
The United States
The Soviet Union
2
3
3
2
0
0
1
1
The pair (2,2) represents the Russians move when they said they would remove their
missiles in Cuba for a trade and that the United States would have to pull their missiles out of
Turkey, it would be a (win, win) situation for both parties. This is not what would have
happened, Chairman Khrushchev agreed to a plan to remove the Soviet Union missiles from
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Cuba, if the United States declared they would not invade Cuba. Generally, the United States and
the Soviet Union won, however, this move resulted in the (3,0) win towards the United States.
They neither had to remove their missiles from Turkey, invade Cuba, or go to war, so they got
exactly what they wanted, (with the acceptation of overthrowing Castro), but the Soviet Union’s
plan to defend themselves against a nuclear attack from the United States had been ruined,
resulting in the 0 portion of (3,0) for the Soviets.
Chairman Khrushchev’s play was a dominated by the President Kennedy’s move, turning
this game into dominance. The Dominance Theory states that rational players would never make
a move that was able to be dominated. The actions Chairman Khrushchev enacted are
questionable under this theory. The reason he played a move that literally handed the United
States the game, is unexplainable and does not hold true to the theory behind Game Theory. He
knew the payoff would be that of a (3,0).
Chairman Khrushchev played a dominated move due to multiple factors, including his
staff and the situation. The imposition of the quarantine, mixed with the burden of his own
generals and military advisors telling instructing him to coincide, acceded his better judgment
(Roberts). The larger goal of putting missiles in Cuba was to protect Cuba from a United States
nuclear attack. Because he listened to his Generals and cracked under the pressure of the
quarantine, Khrushchev failed to remember his ultimate goal, which, in turn, played out in the
United States favor (Barns). If he would have remained persistent and made the United States
remove their missiles from Turkey, for the Soviets to remove their missiles from Cuba, the
payoff would have been exponentially higher, resulting in a (2,2) tie. If anything though, it
makes more sense based on game theory for Chairman Khrushchev to have left his nuclear
warheads stable and began to prepare for nuclear warfare, which would have resulted in a higher
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payoff (1,1) than the (3,0) that he accepted. In long term aspects though, the resulting war would
have proved to be a lose, lose (0,0) situation for both. At the time nevertheless, it would have fit
into the game theory model.
Methods
Participants:
The study of the Cuban Missile Crisis and the analysis of such events were designed
upon the actions between the United States, Cuba, and the Soviet Union. These three participants
were not chosen, because their actions were based on real life, high level security threats. They
were not aware at the time that their actions would be analyzed and subsequently they did not
request payment, or any other accreditation. The participants in the analysis of the Game Theory
represent the quantitative data in which the game is based. The participants are analyzed based
on their actions, reactions, and the outcomes of the game. This study does not discriminate, nor
does it purposefully exclude other factors in which the game does not revolve around.
Materials:
The Game Theorial analysis of the Cuban Missile Crisis required only books and paper in
which information regarding the actions of the players (participants) resided.
Procedure:
This analysis started simply with a brief research period of Game Theory, then research
of each key individual player, then the actions of each player together. The analysis derives
directly from the information produced by the research conducted. The study derived results
based on the analysis of the participants moves during the game in the real life situation that
transpired. This study is based solely on past events and therefore no present day study/play is
needed.
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Discussion
This study proved the thesis that the Cuban Missile Crisis played out in favor of the
United States. When analyzed by Game Theory, it is important to note that the Soviet Union
played an unsuccessful move to gain a (2, 2) outcome rather than the (3,0) outcome that was
consequential. Game theory analysts note that every game deals with rational players, who make
moves that are not able to be dominated, yet the Soviet Union did. When they Soviets played
their move (that the United States vowed not to enter Cuba) it is clear that this was an irrational
decision. It allowed the United States to dominate the Soviets by keeping them in the range of
the missiles, while not being in the Soviets range. The second play for the Soviet Union was that
they would only take their missiles out of Cuba if the United States took their missiles out of
Turkey. This play would directly result in a (2, 2) game, where the United States would benefit
from the Soviets taking their missiles out of Cuba, but forfeit their troops in Turkey. Inversely,
the Soviet Union would do the same. The Soviet Union though, chose a play in which derived a
(3, 0) win for the United States, in which the United States simply agreed to not invade Cuba.
The study produced had limitations though, without an in-depth knowledge of Game Theory and
the decision process behind Chairman Khrushchev, it is difficult to fully expand this topic.
However, with this study, it is evident for future research that the models created by the Decision
Theory or Game Theory will not always be correct. The events that transpired during those
frightful days in October of 1962 have taught us many things, and when analyzed can teach us
how foreign countries can react when facing the United States of America.
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References
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