### Exploring the Prisoner's Dilemma

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?

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