Tutorial 6
GLGSAR001
Question 1
1.1 The Nash Equilibrium is DP, DP. It is a Prisoner’s Dilemma Game.
1.2 Yes, this is because as they are releasing a product every for the next 18 months, it is a
finite set of repetitions. There is a set of sequential interactions. This is backward
induction. In the 18th period, the stores know that there will be no future loss and
therefore decide to maintain cooperation and play DP. In the 17th period, the last period,
the stores will realize that there will be no future loss playing DP and continue to play DP
cooperatively.
1.3 If the game is repeated infinitely and both players (stores) adopt the Grim conditional
strategy, players’ incentives will change. The Grim Strategy means that the stores will
start by playing Cooperate, where they will choose MR, they will continue playing
Cooperate until the rival or other store defects and choose DP. Then if their rival defects,
the store punish him by choosing the Defect strategy in every round for the rest of the
game. Therefore, they will defect forever.
If one of the stores defects and chooses DP, they will get a payoff of 150 instead of instead
of 120. Marginal gain: 30.
If Weasley Wizard Wheezes defects, Gambol & Japes will do the same and defect. Marginal
loss (120-75) = R45.
45
Therefore, it is worth it if 30 > 𝑟
𝑟 > 1.5 = 150%
Therefore, the stores will not choose to defect at an interest rate of 150%.
1−𝑝𝜹
1.4 𝑅 = 𝒑𝜹
𝑝 = 0.6
𝑟 = 0.125
1
𝛿=
1+𝑟
1 8
𝛿= =
1 + 0.125 9
8
1 − 0.6 (9)
𝑅=
8
0.6 ( )
9
0.875 = 87.5%
GLGSAR001
Question 1
1.1 The Nash Equilibrium is DP, DP. It is a Prisoner’s Dilemma Game.
1.2 Yes, this is because as they are releasing a product every for the next 18 months, it is a
finite set of repetitions. There is a set of sequential interactions. This is backward
induction. In the 18th period, the stores know that there will be no future loss and
therefore decide to maintain cooperation and play DP. In the 17th period, the last period,
the stores will realize that there will be no future loss playing DP and continue to play DP
cooperatively.
1.3 If the game is repeated infinitely and both players (stores) adopt the Grim conditional
strategy, players’ incentives will change. The Grim Strategy means that the stores will
start by playing Cooperate, where they will choose MR, they will continue playing
Cooperate until the rival or other store defects and choose DP. Then if their rival defects,
the store punish him by choosing the Defect strategy in every round for the rest of the
game. Therefore, they will defect forever.
If one of the stores defects and chooses DP, they will get a payoff of 150 instead of instead
of 120. Marginal gain: 30.
If Weasley Wizard Wheezes defects, Gambol & Japes will do the same and defect. Marginal
loss (120-75) = R45.
45
Therefore, it is worth it if 30 > 𝑟
𝑟 > 1.5 = 150%
Therefore, the stores will not choose to defect at an interest rate of 150%.
1−𝑝𝜹
1.4 𝑅 = 𝒑𝜹
𝑝 = 0.6
𝑟 = 0.125
1
𝛿=
1+𝑟
1 8
𝛿= =
1 + 0.125 9
8
1 − 0.6 (9)
𝑅=
8
0.6 ( )
9
0.875 = 87.5%
