Netflix and Hulu are deciding what to charge for their online streaming services. Each streaming service can choose a price of either $9 or $12 per month. There are 10 million potential customers. Of these 10 million, 1 million are loyal Netflix customers and another distinct 1 million are loyal Hulu customers. The remaining 8 million consumers will choose the streaming service that is charging the lower price. If the prices are the same, the two firms will split the market, 5 million customers each. The marginal cost of providing service for each company is 0.

a) Suppose the two companies interact only once, and that they make their decisions simultaneously. Describe the game in matrix form and find the Nash equilibrium.

b) Now assume this is a repeated interaction where each firm chooses $9 or $12 at the beginning of each month. Describe clearly (in words) possible strategies of each player that could sustain a "cooperative" arrangement in which the price at $12 each month. (In particular, specify how the two companies should "agree" to play the game, and what each would do in case anyone deviates or cheats on the agreement.)

c) Suppose that the firms' monthly discount factor is r. Find the conditions under which the cooperative agreement can be sustained.

Now Amazon has decided to enter the streaming services market with Amazon Video, which also has a marginal cost of 0. Amazon also has a choice of setting a price of $9 or $12, and would also have 1 million loyal customers for their video services. Therefore, if all three firms set the same price, they will split the entire market.

d) Again treating this as a repeated interaction (but now between Hulu, Netflix, and Amazon, under what conditions on would all firms pricing at $12 be sustainable?

e) Using your answers from (c) and (d), is cooperation among the firms easier or harder after Amazon enters the market? Does this make sense? Explain.