Answer Key
First Midterm Examination:
Econ 101
Richard Buddin
Winter 2008
Please answer all questions.
The questions are in no particular order.
If you do not
understand a question, you should skip it and return to it later in the exam.
1.
Consider the following payoff matrix between two players:
Player 2
Left (L) Middle (M) Right (R)
Top (T)
7,3
6,1
3,4
Player 1
Center (C)
6,5
8,2
2,0
Bottom (B)
5,0
4,7
9,4
a)
Find the Nash equilibrium value or values for the game if the players act
simultaneously.
b)
Suppose that the game in part a is played sequentially, and player 2 goes first.
What strategy should player 2 choose to maximize its payoff?
Is player 2
better off playing first or second?
c)
Now consider the new game in the payoff matrix below.
Find the mixed
strategies solution to the game.
Player 2
Left (L) Right (R)
Player 1
Top (T)
6,5
2,9
Bottom (B)
1,8
4,3
d)
What is the probability of each outcome occurring in the game in part c (find
the probability of TL, TR, BL, and BR)?
Find the expected payoff to the
mixed strategy solution.
Answer:
a)
There are no Nash equilibrium values in this 3x3 game, if it is played
simultaneously.
b)
If player 2 plays first, then player 2’s best strategy is to play R and earn 4 at BR.
a.
If player 2 plays L, then player 1 chooses T.
The payoff to player 2 is 3.
b.
If player 2 plays M, then player 1 chooses M.
The payoff to player 2 is
2.
c.
If player 2 plays R, then player 1 chooses B.
The payoff to player 1 is
4.
If player 2 lets player 1 play first, then player 1 will pick the strategy that
maximizes his/her payoff.
In this case, player 1 will choose M(see below).
Given this choice by player 1, player 2 will choose L and earn a payoff of 5
a.
If player 1 plays T, then player 2 chooses R.
The payoff to player 1 is
3.
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If player 1 plays C, then player 2 chooses L.
The payoff to player 1 is
6.
c.
If player 1 plays B, then player 2 chooses M.
The payoff to player 1 is
4.
The best strategy for player 2 is to let player 1 play first, so he/she earns 5 at
ML (instead of 4 at BR if player 2 plays first).
c)
P
T
=5/9
≈
0.555556, P
L
=2/7
≈
0.285714.
d)
Pr(TL)=10/63, Pr(TR)=25/63, Pr(BR)=8/63, Pr(BL)=20/63.
Payouts:
player
1
≈
3.142857, player 2
≈
6.33333.
2.
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 Winter '08
 Buddin
 Microeconomics, Game Theory, deadweight welfare loss

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