Delphin has developed a new video game that can be produced with two technologie
ID: 1203226 • Letter: D
Question
Delphin has developed a new video game that can be produced with two technologies having the costs C = 10 + 8Q and C = 60 + 2Q . The alpha () technology is well known, while the beta () 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?
Explanation / Answer
a) demand P = 20-Q
revenue = price X quantity
R = (20-Q)Q
R = 20Q - Q2
Marginal revenue = 20 - 2Q
cost of alpha technology = 10+8Q
marginal cost of alpha technology = 8
cost of beta technology = 60+2Q
marginal cost of beta technology = 2
MR = MC
20 - 2Q = 8
12 = 2Q
Q = 6 units with alpha technolgy
20 - 2Q = 2
2Q = 18
Q = 9 with beta technology
Price = 20 - Q
Price of alpha technology = 20 - 6
Price of alpha technology = 14
price of beta technology = 20 - 9
price of beta technology = $ 11
Profit of alpha technology = (20-q)q - [ 10+8Q]
profit of alpha technolgy = (20-6)6 - [ 10 + 8 X 6]
profit of alpha technolgy = $ 26
profit of beta technology = (20 - 9) 9 - [ 60 + 2Q]
profit of beta technology = $ 21
Delphin should adopt the alpha technolgy .
b) The profits of the two fims will be the same i.e $ 26 because Orpheus knows only alpha technology and will manufacture using alpha technology .
c) If Delphin adopts beta technology and Orpheus enters the markets , the profit of delphin will be $ 21 and profit of Orpheus will be $ 26 as Orpheus can manufacture using alpha technology only .
d) Payoff matrix
The dominant strategy is the Nash equilibrium i.e no matter which strategy Delphin chooses , Orpheus can choose only alpha technology as beta technology is not known to Orpheus . Delphin also chooses alpha technolgy as it gives higher payoff compared to beta technology . The payoff for both firms choosing the dominant strategy is ($26,$26) and this is the Nash equilibrium .
Delphin/Orpheus Alpha technology Beta Technology Alpha technology $26,$26 $ 26, Unknown to Orpheus Beta Technology $21,$26 $21, Unknown to OrpheusRelated Questions
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