Economics 1200
Spring 2010
Homework #1 Answers
1.
a. (.5 point) The normal form of the game is:
Warden
Guards at Wall
Regular Inspections
Prisoner
Climb Wall
1, 1
1, 1
Dig Tunnel
1, 1
1, 1
The game is zero, or constant sum
b.
(.5 point) The extensive form version of the simultaneous move game is:
The dashed line represents the information set for the Prisoner.
c.
(.5 point) The mutual best response is to randomize the strategy choices. Prisoner plays Climb
Wall with probability .5 and Dig Tunnel with probability .5 and Warden plays Guards at Wall
with probability .5 and Regular inspections with probability .5.
d. (.5 point) The extensive form version of the sequential move game where the warden is the
first mover looks like the tree depicted above but without the information set, so the 2
nd
mover,
the Prisoner, knows what the Warden has chosen prior to making his (the Prisoner’s) move.
The rollback solution is that if Warden chooses to guard the wall, the Prisoner chooses Dig
Tunnel and if Warden chooses regular inspections, Prisoner chooses Climb Wall.
2. This game is a Prisoner’s Dilemma.
a. (.5 point)
Here is one possible parameterization of the game:
Rita’s
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No Rewards Card
Rewards Card
Bruster’s
No Rewards Card
2, 2
0, 3
Rewards Card
3, 0
1, 1
b. (.5 point) Both players have a dominant strategy: offer rewards card.
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 Spring '09
 BayeMichael
 Economics, Game Theory, Veto, Albus N

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