University of California, Berkeley POL SCI MISC Module 3 hw
Question One (10 total points):
Do regular police patrols reduce crime? Some people claim that police patrols reduce crime by deterring potential
criminals--- that is, people who would otherwise commit crimes will decide not to because the risk if getting caught is
too high. Others argue that police time would be better used investigating crimes that have occurred rather than
increasing regular police patrols.
To investigate this you have an assistant interview both police and people (including criminals) and construct a game
with the payoffs indicated on the following game tree. The basic thing to note is that high patrols increase the cost of
committing a crime, but also increase the cost for police. Payoffs are listed as (Police payoff, Person payoff).
[2 pts] What strategy should the police choose? What will be the payoffs for each player if both players choose
rationally? (Show your work.) Do not commit
Commit
-1 0
-2 2
The criminal course of action depends on strategy of police. If a high patroll strategy is taken, then the criminals best
action would be do not commit (-1,0). Now if the police takes on low patrol, the crime will be commited and the payoff
would be (-2,2). Therefore, the right policy would be to go to High patrol (-1,0).
[2 pts] Assume the police and the people decide their strategies without knowledge of the other party’s choice. Write
out the strategic (tabular) form of this simultaneous game in the space below, being sure to include the payoffs in the
appropriate cells.