It has been observed that companies that choose an IPO to raise capital see the price of their shares rise rapidly in the first days of trading, which means that they have been sold at too low a price or even sold off. For example, when Visa was floated on the New York Stock Exchange in March 2008, the share, listed at 44 dollars, very quickly rose to 65 dollars (+47.73%) from the first day. This phenomenon, which seems to contradict the paradigm of efficient markets, has received many explanations, but game theory in a situation of asymmetric information can shed some interesting light.

The phenomenon of undervaluation can be interpreted in the light of asymmetric information theory. The main hypothesis is that the company has better information on its future financial flows than investors, by definition external. The issuer of shares (the company) signals its true value by offering shares at a discount, and retaining a portion of the issued shares in its portfolio.

Build a simple model of signal sets to represent this situation, with two types and two possible actions.

Give the decision tree corresponding to the game.

Investigate the existence of mixing and separating equilibria in the game you have built.