Two Firms, A and B, have to decide whether to enter a market and, if entering, whether to price high or low. All decisions are made simultaneously, that is, on January 1 at 10:00 AM each firm must announce stay-out or price-high or price low. A firm that stays out earns 0. A firm that prices high earns 8 if the other firm stays out, 2 if the other firm prices high and -3 if the other firm prices low. A firm that prices low earns 4 if the other firm stays out, 4 if the other firm prices high and -1 if the other firm prices low.
a. Write out the bimatrix (normal) form of the game.
b. Find a mixed strategy Nash equilibrium. How do we know that there is a mixed strategy Nash equilibrium for this game?
c. What are the expected earnings for each firm in equilibrium?