4.2. Game theory (Prisoner's dilemma). Often, many sectors in an economy have two main rivals, battling it out in the marketplace. There can be rivalry such as between Apple and Samsung in Phones and Laptops. Suppose Apple plans to cut its price. Samsung will likely follow suit to retain its market share. This may end up with low profits for both companies. A price drop by either company may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if Apple drops its price but Samsung continues to keep prices high, Apple is defecting, while Samsung is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, Apple may win market share and earn incremental profits by selling more. Assume that the incremental profits that accrue to Apple and Samsung are as follows: If both keep prices high (Cooperate), profits for each company increase by AED200 million (because of normal growth in demand). If one drops prices (defects) but the other does not (cooperates), profits increase by AED450 million for the former because of greater market share and are unchanged for the latter. If both companies reduce prices (defect), the increase in tele services offsets the lower price, and profits for each company increase by AED50 million. The profit matrix for Apple vs. Samsung (in millions) Samsung High price (Cooprate) Low price (Defect) 200 450 High price (Cooprate) 200 Apple 50 Low price (Defect) 450 50 Note: Profit for Apple is shaded in blue, while the unshaded area is for Samsung. Question: In the above strategic game, find the Nash equilibrium. Clearly explain your answer.
4.2. Game theory (Prisoner's dilemma). Often, many sectors in an economy have two main rivals, battling it out in the marketplace. There can be rivalry such as between Apple and Samsung in Phones and Laptops. Suppose Apple plans to cut its price. Samsung will likely follow suit to retain its market share. This may end up with low profits for both companies. A price drop by either company may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if Apple drops its price but Samsung continues to keep prices high, Apple is defecting, while Samsung is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, Apple may win market share and earn incremental profits by selling more. Assume that the incremental profits that accrue to Apple and Samsung are as follows: If both keep prices high (Cooperate), profits for each company increase by AED200 million (because of normal growth in demand). If one drops prices (defects) but the other does not (cooperates), profits increase by AED450 million for the former because of greater market share and are unchanged for the latter. If both companies reduce prices (defect), the increase in tele services offsets the lower price, and profits for each company increase by AED50 million. The profit matrix for Apple vs. Samsung (in millions) Samsung High price (Cooprate) Low price (Defect) 200 450 High price (Cooprate) 200 Apple 50 Low price (Defect) 450 50 Note: Profit for Apple is shaded in blue, while the unshaded area is for Samsung. Question: In the above strategic game, find the Nash equilibrium. Clearly explain your answer.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:4.2.
Game theory (Prisoner's dilemma). Often, many sectors in an economy have two main
rivals, battling it out in the marketplace. There can be rivalry such as between Apple and
Samsung in Phones and Laptops. Suppose Apple plans to cut its price. Samsung will likely
follow suit to retain its market share. This may end up with low profits for both companies. A
price drop by either company may thus be construed as defecting since it breaks an implicit
agreement to keep prices high and maximize profits. Thus, if Apple drops its price but
Samsung continues to keep prices high, Apple is defecting, while Samsung is cooperating (by
sticking to the spirit of the implicit agreement). In this scenario, Apple may win market share
and earn incremental profits by selling more.
Assume that the incremental profits that accrue to Apple and Samsung are as follows:
If both keep prices high (Cooperate), profits for each company increase by AED200 million
(because of normal growth in demand).
If one drops prices (defects) but the other does not (cooperates), profits increase by
AED450 million for the former because of greater market share and are unchanged for
the latter.
If both companies reduce prices (defect), the increase in tele services offsets the lower
price, and profits for each company increase by AED50 million.
The profit matrix for Apple vs. Samsung (in millions)
Samsung
High price
(Cooprate)
Low price
(Defect)
200
450
High price
(Cooprate)
200
Apple
50
Low price
(Defect)
450
50
Note: Profit for Apple is shaded in blue, while the unshaded area
is for Samsung.
Question: In the above strategic game, find the Nash equilibrium. Clearly explain your answer.
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