PD - The Prisoners'Dilemma and the Problem of Cooperation...

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1 The Prisoners ’ Dilemma and the Problem of Cooperation One of the central problems of international politics is the problem of cooperation. How can governments reach agreements that make them better off? Arms 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. In other words, there are gains to be had from international cooperation to limit military expenditures. Achieving these gains is difficult, however, due to the structure of the international system. 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 so difficult. 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 economists. 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 weapons. In the terminology of game theory, we say that each government has two strategy choices: build nuclear weapons, which we will denote as b , not build nuclear weapons, which we will denote as n . Two governments with two strategy choices each generates the two-by-two matrix depicted in figure 1. Memorize this matrix because it is critically important. Each cell in this matrix corresponds to a combination of American and Soviet strategies, and these strategy combinations produce real-world outcomes. Figure 1: The Prisoners ’ Dilemma and Arms Races United States Not Build Build Not Build n,n (3,3) n,b (1,4) Soviet Union Build b,n (4,1) b,b (2,2) Preference Orders: Soviet Union: bn > nn > bb > nb United States: nb > nn > bb > nb
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2 We can describe these outcomes starting in the top left cell and moving clockwise. It is important to say a word about the notation we will use before we proceed. By convention we list the row player = s (the player who selects its strategy from the rows of the matrix) strategy choice first and the column player
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This note was uploaded on 03/31/2008 for the course POLI 150 taught by Professor Mosley during the Spring '08 term at UNC.

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PD - The Prisoners'Dilemma and the Problem of Cooperation...

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