Charles B. Cadsby, Murray Frank, Vojislav Maksimovic, Review of Financial Studies 3(3), 315-342

(1990)

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?

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)

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

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.

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) = 300 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

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

Potential belief #1: Both firms undertake all projects.

Investors demand:• s* (0.5 x 1250 + 0.5 x 750) = 300 s* =

30% Firms get:

• 70% of 1250 = 875, if H undertake• 70% of 750 = 525, if L undertake

Beliefs work!

No New Project

With New Project

H Firms 625 1250

L Firms 300 750

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 750 = 450, if L undertake

Beliefs do not work.

No New Project

With New Project

H Firms 625 1250

L Firms 300 750

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

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

Potential belief #1: Both firms undertake all projects.

Investors demand:• s* (0.5 x 625 + 0.5 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 625 1250

L Firms 300 750

No New Project

New Project

H Firms 200 625

L Firms 50 375

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 625 1250

L Firms 300 750

No New Project

New Project

H Firms 200 625

L Firms 50 375

No New Project

New Project

H Firms 200 625

L Firms 50 375

(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.