### Exploring the Prisoner's Dilemma, II

8. The prisoner's dilemma is widely used to illustrate many
things. Do a search on the internet for the term "prisoner's
dilemma." From the links you are given, find a topic that the
prisoner's dilemma illustrates and which is not one discussed in our
readings here.

9. The discussion of the commons suggested that there was a
tendency to overgraze land open to all.

a) Suppose that there are only two herders but that each
could control up to 300 cattle. Would this change the conclusion?
(Hint: Use the table in the discussion
of the commons. Draw a payoff matrix assuming that the
strategies are "Graze 200" and "Graze 300." Then notice that this
is a case in which there are many plays in the game, not just
one.)
b) Suppose that there are 100 herders as in the original
example, but that the king demands 20% of milk production as a
tax. What would he do if he wanted to maximize his tax
receipts?

10. It is rush hour in Chicago and you want to go home. You have
two routes you can travel. One is not congested but has traffic
signals. If you use it, you will arrive home in 30 minutes. You will
not slow down any other driver. The other route is the freeway, which
is becoming crowded. If you use it, you will make it more congested
and slow down 200 other drivers by five seconds. You will also arrive
home in 25 minutes. Assume that the pleasantness or unpleasantness of
both routes is identical. Which route will you choose? From the point
of view of all people who your decision affects, which is the best
decision? Can you see that this is a situation with the same logic as
the hand/fist game has?

11. Substitute teachers are not treated with the same respect by
high-school students as are regular teachers. Explain why in terms of
the various stories of the prisoner's dilemma that we have seen so
far.

12. The website http://serendip.brynmawr.edu/playground/pd.html
allows you to play a multi-round prisoner's dilemma game with the
website as the other party. Play it and see if you can discover what
strategy the website is using.

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