Dr. Chak-Tong Chau
Fulbright Guest Lecture Materials
4
Usefulness of Information
How do we know, a priori, that information is “useful”?
Consider the following payoff structure (known to all):
Y1
{S1}
Y2
{S2, S3}
Y3
{S4, S5, S6}
This new information system partitions the matrix as follows
Signal: Y1
Y2
Y3
S1
S2
S3
S4
S5
S6
e1=10 2
3
3
4
5
5
e2= 5 2
2
3
4
4
5
Question: Are the signals, Y1,,Y2 and Y3 useful?
Consider this new contingent contract (corresponding payoffs):
Prob. e1=0 e2= 5
e3= 6
S1 0.25
0 14,722 (20,000) 14,722 (20,000)
S2 0.25
0 14,722 (20,000) 20,544 (30,000)
S1
S2
S3
S4
Expected Expected
Prob. 0.25
0.25
0.25