Equilibrium with asymmetric information

Consider an economy in which there is initially one firm, HealthyBreakfast, in the market for breakfast cereal. A new firm, TastyCereal, is deciding whether to enter the market, which would then change the market to a duopoly.

HealthyBreakfast's costs of production are either high or low; if HealthyBreakfast has low costs, then it will be able to charge a lower price than TastyCereal, and TastyCereal will earn negative profit from entry. If HealthyBreakfast has high costs, however, then TastyCereal will be able to compete, earning profits of $6 million and reducing HealthyBreakfast's profits to $2 million. The payoffs (in millions) from the four possible outcomes are given in the following diagram (HealthyBreakfast's Payoff, TastyCereal's Payoff).

The diagram shows this game: First, luck and past investments (or "nature") determine whether HealthyBreakfast has high or low costs; then, TastyCereal decides whether to enter the market (without being able to observe HealthyBreakfast's costs).

Nature HealthyBreakfast with High Costs HealthyBreakfast with Low Costs TastyCereal A TastyCereal No Entry Entry No Entry Entry $8. $0 $2, $6 $12, $0 $6, -$2