Econ 171 Spring 2010
Some student questions about PS1 and my responses
Problem 4)
Student question omitted.
Here is the response, though:
You are right that there are no PSNE, but there still can be MSNE.
It is a good idea to
look for dominated strategies to eliminate, as you did, but you are also right that we
cannot eliminate any.
I'll try to explain how to start looking for the MSNE.
Ok, first let's think about 2 mixing, because 2 has only 2 choices, so it may be simpler.
For 2 to mix, 2 has to be indifferent between R and L.
If 1 chooses A, 2 doesn't care, but
if 1 chooses B or C, 2 does care.
Notice that only if prob(B) = prob(C) will 2 be
indifferent b/w L and R.
So we know that 1 has to choose B and C with equal probability.
Now consider two cases.
1)
prob(B) = prob(C) > 0  what does 2 have to do for 1 to be willing to mix?
If 2
does this, what is 1's best response?
2)
prob(B) = prob(C) = 0 what does 2 have to do for 1 to prefer A to both B and
C?
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 Fall '08
 Charness,G
 Game Theory, PROB, efficient strategy profile

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