Problem Set #9
- PlSc 349
- Due: Tuesday, 9 November 2010
- [7 points] Problem U12.2
- [10] Problem U12.3
- [10] Problem U12.4
- [10] Problem U12.5
- [8] [from Johnson 2002]
In the following environments, a large number of identical players choose
simultaneously between two pure strategies; they cannot randomize. In each case,
graph the payoffs of the two strategies against the population frequency of the
first strategy in a way that is consistent with the verbal description. Then use
your graph to determine what pattern (or patterns) of behavior will emerge in the
long run, and whether the pattern(s) that emerge(s) will be Pareto-efficient, in
the sense of maximizing all players' average expected payoff. If not, what
method would you use to solve the “problem”?
a. Each person can either install a car alarm in his car or not. Car alarms
are highly effective when only a few cars have them, but (because people ignore
them when they hear them go off too often) they are ineffective when most of
the cars have them.
b. There is a wall running through the center of your city, left over from
the Cold War. Each person can either try to tear down the wall or ignore it.
Everyone hates the wall, but everyone knows that if only a few people try to
tear it down the government will arrest them and send them to jail. However,
everyone also knows that if more than a few people try to tear it down, the
government is unlikely to punish them.
c. Each person can either shirk (effort level 1) or work hard (effort level 2).
Each wishes to minimize the distance between his own effort level and the
average effort level in the population (in other words, his payoff is minus
this distance).
d. Answer part c. again, but assume that each person wishes to minimize the
difference between his own effort level and one-half the average effort level
in the population.
- [5] Problem S12.6
- [for future planning] Which problem was most useful in learning
the concepts? Which problem was least useful?
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