Mr Jaša Andrenšek
a)
If Alice chooses not buy, best response of Caterpillar is to choose bad. And if Caterpillar chooses bad, best response of Alice is to choose not buy. Therefore, pure strategy Nash equilibria is bottom right corner. Not buy from Alice and bad from Caterpillar.
b) No, there isn't a trigger strategy that induces buy/good for 10 periods.
If this was infinitely repeated interaction, δ would equal to 1/3, computed from trigger condition
Equation. Using the same tools, we derive following equation for 10 repeated interactions: δ10 -1/ δ -1 > πD/πC
We know that for caterpillar, meaning right side of equation is above 1. Looking at the left side, knowing δ is below 1, I conclude δ that would result in buy/good doesn’t exist.
9 periods make no difference. Again trigger strategy doesn’t exist.
c) Again taking standard trigger condition for δ and equal δ to 1 we derive:
1 > (πD - πC) / (πD – πN) which tells us that πD - πC should be lower than πD - πN. In effect giving, πC > πN. If this condition is meet with both Alice and Caterpillar then we could obtain a trigger strategy Buy/Good. This condition is indeed met, so we can obtain Buy/Good in this case.
d) Again taking our standard condition δ > (πD - πC) / (πD – πN) and plug the relevant for Caterpillar (only Caterpillar is relevant as Alice would never deviate if Caterpillar cooperates) respectively we obtain δ > 1/3. The range is between 1/3 and 1 for δ. We know δ = 1/1 +r which gives the maximum value of interest rate 200%. Range for is 0< r <2.
e) δ = P/ 1+r
P= 0.70 δ = 1/3 r=1.1212 Cooperative equilibrium is still possible for values of r from 0 to 1.12, which means the maximum level of interest rate of 112%.
2.
a)
Pure strategy equilibria of the game are: M&L (best response of student 1 is L if student 2 chooses M and vice-versa), H&H (best response of student is H if student 2 chooses H and vice-versa). Efficient outcome is not
If Alice chooses not buy, best response of Caterpillar is to choose bad. And if Caterpillar chooses bad, best response of Alice is to choose not buy. Therefore, pure strategy Nash equilibria is bottom right corner. Not buy from Alice and bad from Caterpillar.
b) No, there isn't a trigger strategy that induces buy/good for 10 periods.
If this was infinitely repeated interaction, δ would equal to 1/3, computed from trigger condition
Equation. Using the same tools, we derive following equation for 10 repeated interactions: δ10 -1/ δ -1 > πD/πC
We know that for caterpillar, meaning right side of equation is above 1. Looking at the left side, knowing δ is below 1, I conclude δ that would result in buy/good doesn’t exist.
9 periods make no difference. Again trigger strategy doesn’t exist.
c) Again taking standard trigger condition for δ and equal δ to 1 we derive:
1 > (πD - πC) / (πD – πN) which tells us that πD - πC should be lower than πD - πN. In effect giving, πC > πN. If this condition is meet with both Alice and Caterpillar then we could obtain a trigger strategy Buy/Good. This condition is indeed met, so we can obtain Buy/Good in this case.
d) Again taking our standard condition δ > (πD - πC) / (πD – πN) and plug the relevant for Caterpillar (only Caterpillar is relevant as Alice would never deviate if Caterpillar cooperates) respectively we obtain δ > 1/3. The range is between 1/3 and 1 for δ. We know δ = 1/1 +r which gives the maximum value of interest rate 200%. Range for is 0< r <2.
e) δ = P/ 1+r
P= 0.70 δ = 1/3 r=1.1212 Cooperative equilibrium is still possible for values of r from 0 to 1.12, which means the maximum level of interest rate of 112%.
2.
a)
Pure strategy equilibria of the game are: M&L (best response of student 1 is L if student 2 chooses M and vice-versa), H&H (best response of student is H if student 2 chooses H and vice-versa). Efficient outcome is not