Section X: Asymmetric Information
Daniel Egel
November 16, 2008
1
Review and the Folk Theorem
1
I’m going to motivate the
Folk Theorem
using an example we have seen from before.
Player 1
Player 2
E
F
G
A
5,4
1,6
1,1
B
7,1
2,2
0, 0
C
2,3
0, 3
0, 2
1. What is the stage game Nash here? What are the minmax payoffs for each player?
2. If we allow grim trigger strategies, for what values of
δ
can (
A, X
) be played repeatedly?
This is a Nash equilibrium.
3. Now if we only allow for Nash trigger strategies, for what values of
δ
can (
A, X
) be played
repeatedly? This is a Subgame Perfect Equilibrium.
4. Is there some
δ
so that (
B, X
) is a Nash equilibrium? How about a SPE?
•
Hint: You don’t need to find it!
•
Just use the
Folk Theorem
!
That is, as long as their is a credible threat, we can
always find an equilibrium for that point.
2
An Example from an Old Exam
2.1
A Market for Lemons
In many situations the seller knows the quality of the good they are trying to sell but the buyer
does not. This question examines the effect of this asymmetry. A buyer and seller are negotiating
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