Delphin has developed a new video game that can be produced with two technologies having the costs Cα = 10 + 8Q and Cβ = 60 + 2Q . The alpha (α) technology is well known, while the beta (β) technology is known only to Delphin. Demand is estimated as P = 20 – Q, where Q is industry output.
a. Suppose Delphin is certain that it will have a monopoly on the new game. Which technology should Delphin adopt? What are its profits with each technology? Delphin has learned that its rival, Orpheus, is considering entering this market using the alpha technology. If Orpheus enters, the firms will play a Cournot game (simultaneously choosing quantities).
b. If Delphin adopts the alpha technology and Orpheus enters, what are the profits of the two firms?
c. If Delphin adopts the beta technology and Orpheus enters the market, what are the profits of the two firms?
d. Draw out the extensive form sequential game (game tree) in which Delphin moves first to choose a technology, followed by Orpheus’s choice to enter or not. Use your answers to a, b, and c above to determine the payoffs to each possible outcome. What is the Nash Equilibrium of this sequential game?