Consider the following three player game, recaling that a strategy profile (A, B, B), for example, means that player 1 plays A, player 2 piays B, and player 3 plays B. In this scenario, each player represents a company which m whether to adopt a new technology "B", or keep an old technology "A". Each technology has a stand-alone benefit, as well as a "networking benefit". That is, the more people using a specific technology, the more beneficial it is adopt that technology as well. For example, more firms using a specific machine may find it easier to find spare parts or repair people in the area. Lastly, suppose that the networking benefit of the new technology B is yet unce represented by a parameter E. The game can be represented below. А P3 В P2 В А А P2 B А A 3,3,3 2,ɛ, 2 А 2, 2, € 1, ɛ + 3, ɛ +3 P1 P1 B Be + 3,1, ɛ + 3 e+6,8+ 6,ɛ + 6 E + 3,8 +3, 1 B ɛ, 2, 2 For which values of E is (B, B, B) the only Nash equilibrium. O E>3 O E<3 O E>6
Consider the following three player game, recaling that a strategy profile (A, B, B), for example, means that player 1 plays A, player 2 piays B, and player 3 plays B. In this scenario, each player represents a company which m whether to adopt a new technology "B", or keep an old technology "A". Each technology has a stand-alone benefit, as well as a "networking benefit". That is, the more people using a specific technology, the more beneficial it is adopt that technology as well. For example, more firms using a specific machine may find it easier to find spare parts or repair people in the area. Lastly, suppose that the networking benefit of the new technology B is yet unce represented by a parameter E. The game can be represented below. А P3 В P2 В А А P2 B А A 3,3,3 2,ɛ, 2 А 2, 2, € 1, ɛ + 3, ɛ +3 P1 P1 B Be + 3,1, ɛ + 3 e+6,8+ 6,ɛ + 6 E + 3,8 +3, 1 B ɛ, 2, 2 For which values of E is (B, B, B) the only Nash equilibrium. O E>3 O E<3 O E>6
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.5P
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Transcribed Image Text:Consider the following three player game, recalling that a strategy profile (A, B, B), for example, means that player 1 plays A, player 2 plays B, and player 3 plays B. In this scenario, each player represents a company which must decide
whether to adopt a new technology "B", or keep an old technology "A". Each technology has a stand-alone benefit, as well as a "networking benefit". That is, the more people using a specific technology, the more beneficial it is for you to
adopt that technology as well. For example, more firms using a specific machine may find it easier to find spare parts or repair people in the area. Lastly, suppose that the networking benefit of the new technology B is yet uncertain, and is
represented by a parameter E. The game can be represented below:
A
P3
В
P2
B
A
A
P2
B
А 3,3,3
2, ε, 2
А
2, 2, ɛ
1, ɛ + 3, 8 +3
Р1
P1
Be + 3,1, ɛ + 3 e+ 6,ɛ + 6, ɛ + 6
В Е, 2,2
ɛ + 3, ɛ + 3, 1
For which values of E is (B, B, B) the only Nash equilibrium.
O E>3
O E<3
O E>6
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