Homework Answers
A. Let us say the two friends are A & B. A is represented by blue and B is represented by green in the payoff matrix
| Payoff Matrix | |||||
| B | |||||
| Road Bike | Mountain Bike | ||||
| A | Road Bike | 2 | 1 | ||
| 2 | 0 | ||||
| Mountain Bike | 0 | 3 | |||
| 1 | 3 | ||||
Payoff matrix gives us a visual representation of the payoff that each one of the friends gets.
B. Suppose B selects Road bike, A's best selection will be Road bike. Similarly, if B selects Mountain bike, A's best selection will be Mountain bike.
Suppose A selects Road Bike, B's best selection is Road bike, and if A selelcts Mountain Bike, B's best selection will be Mountain bike
So, there is no dominant strategy here.
C. Suppose B selects Road bike, A's best selection will be Road bike. Similarly, if B selects Mountain bike, A's best selection will be Mountain bike.
Suppose A selects Road Bike, B's best selection is Road bike, and if A selelcts Mountain Bike, B's best selection will be Mountain bike
So, No, there are not any weakly dominated strategies as well.
D. Nash Equilibria cant be acheived in this matrix, as there are two high choices, it will be a mixed strategy outcome.
| Payoff Matrix | |||||
| B | |||||
| Road Bike | Mountain Bike | ||||
| A | Road Bike | 2 | |||
| 2 | |||||
| Mountain Bike | 3 | ||||
| 3 | |||||
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