1. An arms race can be seen as a case of a prisoner's dilemma. Draw a payoff matrix showing the results of strategies "less armament" and "more armament" for two hostile nations. (Hint: Assume that war is a result of mistakes: that is, a nation does not go to war if it believes that it will lose. Payoffs then include "stalemate," "dominance," and "subservience.")
2. The prisoners' dilemma is an example of game theory. Search the Internet for "game theory." How is it defined, what is it used for, and who invented it?
3. Game theory introduced the terms "zero-sum game," "positive-sum game," and "negative-sum game." A zero-sum game is an interaction among people where the amount lost equals the amount gained. That means that if one person gains, another person must lose.
a. How do you think a positive-sum game would be defined? How about a negative-sum game?
b. Which of the following are zero-sum situations, which are positive-sum, and which are negative-sum? (Comment: It is possible to disagree with a few of the answers--it all depends on what you count as winnings and losings.)
c. Can you think of other examples of zero-sum interactions? Positive-sum interactions? Negative-sum interactions?
d. Look up zero-sum, positive-sum, and negative sum on the Internet. (You might want to include the word game, or maybe not.) Find at least one example of each that you found.
e. Some people think of the world as a struggle for power. Is this way of looking at the world zero-sum, positive-sum, or negative sum?
4. Economists are a bit unusual because they view the world as basically positive-sum. Why? (Hint: Economists mostly study exchange.) Is that a optimistic or pessimistic way of viewing the world?