Midterm Exam Worksheets With Answers - Prof. James Peck - The Ohio State University, Department Of Economics - 2010 Page 3
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63. (15 points) For the normal-form game depicted below, find each of the
pure-strategy Nash equilibria.
player 2
a
b
c
d
e
v
3,9
1, 8
0, 3
5, 6
2, 3
w
0, 1
6, 3
5,4
4, 3
7, 2
player 1 x
6,8
5, 7
2, 4
1, 1
0, 4
y
1, 5
6, 1
3, 2
7,6
2,6
z
7,4
8, 3
4, 1
4, 0
3, 3
Answer:
For a matrix this big, we need to find the best responses to each strategy of
the other player, which I have underlined in the matrix. For example, to find
player 2’s best response to player 1’s strategy y, we look at player 2’s payoffs
along the row corresponding to y and see that there are two best responses;
both d and e yield a payoff of 6, so both of those numbers are underlined.
For a pure-strategy NE, each player must be best-responding to the other,
so we look for a profile for which both numbers in the cell are underlined. This
game has 3 pure strategy NE: (z, a), (w, c), and (y, d).
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