ECON 100B Lecture 11: Repeated Games and Cartels (Con’t)
17 May 2018
School
Department
Course
Professor
Econ 100B Lecture 11 - May 17, 2018
Repeated Games and Cartels (Con’t)
Problem 1
Two companies HOnda and Suzuki selling motorcycles
Warranties are expensive but it sends a good signal to customers.
If both companies offer warranty then each will earn 20 million as revenue.
If one offers and other does not, then former get 120 million as revenue and the other gets only
10 million.
If no ones offer warranty each will get $50 millions revenue
Suzuki
Honda
Offer Warranty
Doesn’t offer
Offer Warranty
20, 20
120, 10
Doesn’t offer
10, 120
50, 50
a. If the game is played one time, what will be the outcome?
Nash equilibrium: (Offer Warranty, Offer Warranty)
b. If the game is played 3 times, what will be the outcome?
Nash equilibrium: (Offer Warranty, Offer Warranty)
Nash Equilibrium will not change
c. If the game is played in finite number of times, will the cooperative outcome
Payoff stream from cheating:
120 + d (20) + d^2 (20) + d^3 (20) + d^t (20) + …..
2018 + 2019 + 2020 + …………….
Payoff stream from not cheating:
50 + d (50) + d^2 (50) + d^3 (50) + d^t (50) + …..
2018 + 2019 + 2020 + …………….
Firm does not cheat if the payoff stream from not cheating is higher than the payoff from
cheating
50 + d (50) + d^2 (50) + d^3 (50) + ….. > 120 + d (20) + d^2 (20) + d^3 (20) + …..
50 ( d + d^2 + d^3 + …..) > 20 ( d + d^2 + d^3 + …..
(50 - 20) ( d + d^2 + d^3 + …..) > 70
30 ( d + d^2 + d^3 + …..) > 70
d / 1-d > 70/30
d > 0.7
Document Summary
Econ 100b lecture 11 - may 17, 2018. Warranties are expensive but it sends a good signal to customers. If both companies offer warranty then each will earn 20 million as revenue. If one offers and other does not, then former get 120 million as revenue and the other gets only. If no ones offer warranty each will get millions revenue. If the game is played in finite number of times, will the cooperative outcome. 120 + d (20) + d^2 (20) + d^3 (20) + d^t (20) + 50 + d (50) + d^2 (50) + d^3 (50) + d^t (50) + Firm does not cheat if the payoff stream from not cheating is higher than the payoff from cheating. 50 + d (50) + d^2 (50) + d^3 (50) + > 120 + d (20) + d^2 (20) + d^3 (20) +
