MS&E 246: Game Theory with Engineering Applications
Midterm Exam
Feryal Erhun & Ramesh Johari
Winter, 2006
Solutions
1. (10 points; 2.5 points each) Select true or false; you do not need to justify your answer.
(a) In an extensive form game, every SPNE is an NE and every NE is an SPNE.
False – every SPNE is an NE, but not every NE is necessarily an SPNE.
(b) Every dynamic game of perfect information has an SPNE in pure strategies.
True – it can be found using backward induction.
(c) If M is a weakly dominant strategy for player 1 and L is a weakly dominant strategy
for player 2, then (M,L) is a NE.
True – each is a best response to the other.
(d) Every game has at least one efficient NE.
False – see the Prisoner’s Dilemma.
2. (30 points) Consider the strategic form games and answer each question separately.
(a) Consider the following game.
Player 2
L
R
T
(1,1)
(0,0)
Player 1
M
(1,1)
(2,1)
B
(0,0)
(2,1)
i. Does player 1 have a strictly/weakly dominant strategy?
Answer: (3 points)
Player 1 does not have a strictly dominant strategy. How
ever, he has a weakly dominant strategy, M.
ii. Does player 2 have a strictly/weakly dominant strategy?
Answer: (3 points)
Player 2 does not have a strictly/weakly dominant strategy.
iii. Is this game dominance solvable?
Answer: (4 points)
This game is not dominance solvable.
(b) Consider the following game.
1
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Player 2
L
M
R
T
(3,2)
(4,0)
(1,1)
Player 1
M
(2,0)
(3,3)
(0,0)
B
(1,1)
(0,2)
(2,3)
i. Iteratively eliminate all the strictly dominated strategies.
Answer: (5 points)
For player 1, T strictly dominates M, hence we eliminate M
of player 1. Now, R strictly dominates M, hence we eliminate M of player 2.
We obtain the following. Note that, for part (iii), we are going to use this game
as a rational player will not play a dominated strategy as a part of a NE.
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 Winter '07
 JOHARI
 Game Theory, player, Ramesh Johari

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