Midterm Exam Worksheets With Answers - Prof. James Peck - The Ohio State University, Department Of Economics - 2010 Page 2
ADVERTISEMENT
1
2
3
4
5
62. (20 points) For the normal-form game given below, is player 1’s strategy
M dominated? If so, name a pure or mixed strategy that dominates it. If not,
name a belief to which M is a best response.
player 2
X
Y
K
8, 2
0, 0
player 1 L
3, 0
5, 1
M
4, 2
3, 2
Answer:
Player 1’s strategy M is dominated by a mixture of K and L, of the form
(p, 1 − p, 0). To find values of p that work, we must show that player 1 prefers
the mixture when player 2 plays X and when player 2 plays Y. Thus, we must
have
8p + 3(1 − p) > 4 and
0p + 5(1 − p) > 3.
1
The first inequality simplifies to p >
, and the second inequality simplifies
5
2
to p <
. Any p satisfying both inequalities defines a mixed strategy that
5
1
dominates M. For example, p =
corresponds to the mixed strategy, σ
=
1
3
1
2
(
,
, 0).
3
3
2
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education