“Pooling, Separating, and Semiseparating Equilibria in Financial Markets: Some Experimental Evidence” Charles B. Cadsby, Murray Frank, Vojislav Maksimovic, Review of Financial Studies 3(3), 315-342 (1990)

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?

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)

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

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.

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) = 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

Symmetric Information: Cadsby et. al. Results

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

Game 1 – Theoretical Results 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

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 750 = 450, if L  undertake Beliefs do not work. No New Project With New Project H Firms 625 1250 L Firms 300 750

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

Game 1 – Cadsby et. al. Results

Your Results

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

Game 2 – Theoretical Results 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 200 625 L Firms 50 375 No New Project New Project H Firms 625 1250 L Firms 300 750

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

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

Game 2 – Cadsby et. al. Results

Your Results

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.