1. “Pooling, Separating, and Semiseparating Equilibria in Financial Markets: Some Experimental Evidence”
Charles B. Cadsby, Murray Frank, Vojislav Maksimovic, Review of Financial Studies 3(3), (1990)

2. Myers and Majluf (1984)
Question: How do investors and firms deal with asymmetric information?
Firms have information that investors do not about their quality. How do firms and investors interact to fund projects?

3. Myers and Majluf (1984) Two types of firms, i = H, L Each firm gets
Ai if they do not undertake a project
(1-s)(Bi) if they undertake the project
Therefore, firms should undertake a project iff
E(1-s)(Bi) > Ai
Each investor gets
0 if no project is undertaken
sBi – C if they finance the project
Therefore, investors should bid as long as
sE(Bi) > C  s = C/sE(Bi)

4. Myers and Majluf (1984)
With asymmetric information, H firms will have to give more equity than they would with symmetric information.
Pooling equilibria – all projects are undertaken
Amount H firms lose due to uncertainty less than their gain from the project
Separating equilibria – only L firms undertake projects
Amount H firms lose due to uncertainty greater than their gain from the project

5. Cadsby et. al. (1990) Let’s test this experimentally!
When theory predicts a unique equilibrium, will it happen?
When theory predicts multiple equilibria, which will occur?
NB: In the interest of time, I will not discuss semiseparating equilibria or signaling models, though these are important parts of the Cadsby et. al. paper.

6. Symmetric Information: Theoretical Results
If I tell you whether the firm was H or L.
Investors should demand s* such that
s* (1250) = 300  s* = 24% for H firms
s* (625) =  s* = 48% for L firms
Payoffs to firms would be
76% of 1250 = 950 for H firms
52% of 625 = 325 for L firms
Both firms will undertake projects.
No New Project
New Project
H Firms
500
1250
L Firms
250
625

7. Symmetric Information: Cadsby et. al. Results

8. Game 1 – Theoretical Results
I did not tell you whether the firm was H or L.
Now beliefs matter – as an investor, it matters what I believe is, given you offer me a project, the probability that you are H or L.
No New Project
With New Project
H Firms
625
1250
L Firms
300
750

9. Game 1 – Theoretical Results
Potential belief #1: Both firms undertake all projects.
Investors demand:
s* (0.5 x x 750) = 300  s* = 30%
Firms get:
70% of 1250 = 875, if H  undertake
70% of = 525, if L  undertake
Beliefs work!
No New Project
With New Project
H Firms
625
1250
L Firms
300
750

10. Game 1 – Theoretical Results
Potential belief #2: Only L firms undertake projects.
Investors demand:
s* (750) = 300  s* = 40%
Firms get:
60% of 1250 = 750, if H  undertake
60% of = 450, if L  undertake
Beliefs do not work.
No New Project
With New Project
H Firms
625
1250
L Firms
300
750

11. Game 1 – Theoretical Results
Therefore, we should have a pooling equilibrium where every project is undertaken and s* = 30%.
No New Project
With New Project
H Firms
625
1250
L Firms
300
750

12. Game 1 – Cadsby et. al. Results

13. Your Results

14. Game 2 – Theoretical Results
I did not tell you whether the firm was H or L.
Beliefs matter – as an investor, it matters what I believe is, given you offer me a project, the probability that you are H or L.
No New Project
New Project
H Firms
200
625
L Firms 50
375

15. Game 2 – Theoretical Results
Potential belief #1: Both firms undertake all projects.
Investors demand:
s* (0.5 x x 375) = 300  s* = 60%
Firms get:
40% of 625 = 250, if H  undertake
40% of 375 = 150, if L  undertake
Beliefs work!
No New Project
New Project
H Firms
200
625
L Firms 50
375
No New Project
New Project
H Firms
625
1250
L Firms
300
750

16. Game 2 – Theoretical Results
Potential belief #2: Only L firms undertake projects.
Investors demand:
s* (375) = 300  s* = 80%
Firms get:
20% of 625 = 125, if H  do not undertake
20% of 375 = 75, if L  undertake
Beliefs work!
No New Project
New Project
H Firms
200
625
L Firms 50
375
No New Project
New Project
H Firms
625
1250
L Firms
300
750

17. Game 2 – Theoretical Results
Will we see:
Pooling equilibrium, s* = 60%?
Both H and L undertake projects
Separating equilibrium, s* = 80%
Only L undertakes projects
No New Project
New Project
H Firms
200
625
L Firms 50
375

18. Game 2 – Cadsby et. al. Results

19. Your Results

20. Cadsby et. al. Results
(related to the experiments replicated here)
If a unique equilibrium is predicted, it is observed.
If multiple equilibria are predicted, a pooling equilibrium is observed.
Note that it is a bit unclear whether we were acting in accordance with the pooling equilibrium in our Game 1. In our Game 2, the separating equilibrium share value was found in the second experiment (inconsistent with Cadsby et. al.results), but both firms entered the market. This is inconsistent with both the theory and the Cadsby et. al. results.