Problem 2: Game Theory [11 Points] Suppose that a market is made up of two firms, Firm A and Firm B. Each of those firms have zero Fixed Costs (FC) and a fixed Marginal Cost (MC) equal to $10 per unit. Suppose that market demand is given by: Q = 160 - 4p 4. If one of these firms could be a monopolist, what would be their price and quantity? How much profits would they make? [3 points] Now suppose that Firm A and Firm B agree to form a cartel. As part of this cartel agreement, they both produce an equal quantity of the good, and choose their quantity to maximize their joint profits. 5. What quantity does each firm produce here. How much profits does each firm make? [2 points] 6. Suppose now that Firm A decided to cheat on the cartel, and increased their production by an additional 10 units. What happens to the market price, and the profits of Firm A and Firm B? [2 points] Now we are going to convert this to a Game Theory question, where Firm A and Firm B are the two players, and they each choose either (i) Cooperate, where they follow the cartel agreement, and (ii) Cheat, where they increase their production by an additional 10 units. 7. Write out the Game Theory payoff matrix below for this game. Have Firm A's payoffs correspond to rows. Have Firm B's payoffs correspond to columns. It should be clear which player receives which payoff in each cell. [3 points] 8. What are the Nash Equilibria in this game (if any)? [1 point]