The Prisoners ’ Dilemma and the Problem of Cooperation
One of the central problems of international politics is the problem of
How can governments reach agreements that make them better off?
races provide a good example of the problem of cooperation.
On the one hand, if all
governments spend a lot of money on military forces, no government gains any additional
security or is better able to influence others.
Thus, countries are better off if they can
somehow all agree to refrain from engaging in a military buildup— they will enjoy the
same level of security without an arms race as they do with an arms race, but without an
arms race each country saves the resources it otherwise dedicates to the military.
words, there are gains to be had from international cooperation to limit military
Achieving these gains is difficult, however, due to the structure of the
This problem of cooperation is more than a theoretical problem—
throughout the Cold War the United States and the Soviet Union tried, with varying
degrees of success, to cooperatively manage their nuclear competition.
The purpose of
this short reading is to use game theory to demonstrate why international cooperation is
The problem of cooperation in general, and arms races in particular, can be
modeled with game theory.
Game theory is an approach to the study of interdependent
decision-making, often called strategic interaction, developed by mathematicians and
One game in particular, the prisoners
dilemma, has received the most
attention as a model of how strategic interaction in the anarchic international system
creates incentives for governments to enter into arms races and complicates their abilities
to effectively end arms races.
In the prisoners
dilemma, two governments, lets call them the United States and
the Soviet Union must decide whether to build nuclear weapons or not to build nuclear
In the terminology of game theory, we say that each government has two
strategy choices: build nuclear weapons, which we will denote as
, not build nuclear
weapons, which we will denote as
Two governments with two strategy choices each
generates the two-by-two matrix depicted in figure 1.
Memorize this matrix because it is
Each cell in this matrix corresponds to a combination of American
and Soviet strategies, and these strategy combinations produce real-world outcomes.
The Prisoners ’ Dilemma and Arms Races