Question 1: Consider the following problem. DealCo has come up with a gadget and is contemplating whether to advertise during the next Superbowl. Consumers have heard of the gadget but are uncertain of its quality. Given its current price, they are unwilling to try it because of the uncertainty, but would be willing to purchase if they believed that it is high quality with high-enough probability. The marketing department of DealCo has estimated that, if they can persuade consumers to try the product, they will earn $50M in additional profits if the gadget is a high-quality one, while they will earn $20M in additional profits if the gadget is a low-quality one, with the difference arising from converting consumers to repeat customers when they have a good experience. How expensive should the Superbowl ad be so that the potential customers could take seeing the ad as a credible signal of high quality and so try the product?

Question 2: Consider the following situation. British Airways (BA) is currently a monopolist on a route between London and Boston. Virgin Atlantic is currently considering entering the route but does not know the cost structure of BA and so cannot predict the pricing response of BA following entry. However, it can see the current market price charged by BA and try to make an inference about BA's cost structure and thus profitability of entry. In the game, BA knows its cost structure and chooses either a high or a low price. Virgin sees this price, makes an inference about BA's costs and thus profitability of entry, and makes an entry decision. For the parameters, we assume the following.

• For Virgin, entry costs $40, and its profits (excluding entry costs) will be $50 if BA has a high cost and $10 if BA has a low cost of operating. Virgin's goal is to maximize its profits minus entry cost. Not entering gives a payoff of zero.
• For BA, we will parameterize their operating environment so we can pin down the costs and benefits of different pricing choices. Assume that BA's marginal cost of a flight is either MC = 11 (high) or MC = 5 (low). BA knows its costs, but Virgin only knows that it is high with probability 0.6 and low with probability 0.4. BA's current demand for flights is Q(P) = 25 - P. BA's (per period) profits, as long as it is the only firm on the route are given by TI = (P - MC) * Q(P), where P is the price chosen, MC is the cost per flight, and Q(P) is the realized demand for flights given the price. You can solve this to confirm if you would like, but if BA has a high cost, then its profit-maximizing price would be P = 18, giving profits of 49, while if it has low cost, its profit- maximizing price would be P = 15, giving profits of 100. BA's objective is to maximize its profits over the two periods, TIl + TI2, with no discounting between the periods, where in the first period BA is a monopolist, and in the second period either a monopolist or a duopolist, depending on Virgin's entry decision. If BA remains a monopolist, its profit function next period is the same as today. If entry occurs, BA's profits will be 5 if it is the high-cost type and 45 if it is the low-cost type (and the type stays constant across the periods).

(1) Focusing on BA choosing only between the prices of 15 and 18 today (and pricing optimally in the second-period given its costs when there is no further threat of entry), the situation is depicted by the simplified game three below. Complete the tree by entering the correct payoffs for each of the players to the tree (for Virgin, second-period profits minus entry cost, while for BA, the sum of profits during the first and second period).

Enter Enter Virgin BA Virgin P=15 P=18 Don't Don't X5 X2 X3 High 0.6 "nature" X1 Enter Low 0.4 Enter X6 X4 X1 P=15 Don't P=18 BA Don't Figure 1: The extensive-form game for question 2