SABANCI UNIVERSITY
ECON 201 – A
GAMES AND STRATEGY
FIRST MIDTERM
EXAMINATION ANSWERS
March 20, 2007
1.
(
20 points
). It is a fact that “if in a dynamic game no player ever gets the same payoff in
two terminal nodes, then there is a unique bacward induction solution.” Draw the
extensive form of a game in which player 1 moves first and chooses between A and B,
followed by player 2 choosing between ‘left’ and ‘right’ and the game ends. Choose the
payoffs for the two players so that (a) Player 2’s payoffs are all different whereas Player
1 gets the same payoff in two terminal nodes and (b) the game has two backward
induction solutions. Write down the two solutions (with complete strategies).
ANSWER…
#1
A
B
#2
#2
left
right
left
right
(3 , 5)
(2 , 4)
(1 , 7)
(3 , 8)
The payoffs are my choices. Player 2’s payoffs are all different, while Player 1’s gets the
same payoff 3 in the outcome (A,left) and (B,right). The backward induction solutions are,
“Player 2 plays right if B, left if A” in both solutions. Player 1 is indifferent between A and B,
which yields two solutions.
2.
(
25 points
)
In the rural areas around Ithaca, US, farmers put some fresh produce on a
table by the road. There is a cash box on the table and customers are expected to put
money in the box for the vegetables they take. The box is attached to the table (so no one
can make off with the money) and has just a small slit (so money can only be put in, not
taken out.)
Consider the following game, as in the story above. A farmer decides on whether to (a) leave his
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 Fall '12
 SelçukErdem
 Game Theory, Nash, SABANCI UNIVERSITY, payoﬀ

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