Question

Answer A through D, please!

Currently Sam and Carla have the only taxi services in a small town. Both Sam and Carla are thinking about discounting their respective fares by 20% to attract more business.

The possible outcomes of this game are as follows.

First: Sam offers discounts, while Carla does not, which will result in Sam earning $800 in profit and Carla earning $300 in profit.

Second: Sam and Carla both offer discounts, which will result in Sam earning $200 in profit and Carla earning $500 in profit.

Third: Sam and Carla both do not offer discounts, which will result in Sam earning $600 in profit and Carla earning $700 in profit.

Fourth: Carla offers discounts, while Sam does not, which will result in Sam earning $100 in profit and Carla earning $1,000 in profit.

a) Please construct a payoff matrix for Sam and Carla uses the outcomes above. (You can use the Table Function in Word to create a payoff matrix.)

b) Does Sam have a dominant (optimal) strategy? Please explain your answer.

c) Does Carla have a dominant (optimal) strategy? Please explain your answer.

d) Is there an equilibrium (Nash Equilibrium) solution to this problem where we can predict the strategy of both Sam and Carla? Please explain your reasoning.

Answer 1

a) The game above can be presented in the form of a matrix in the following way:

SAM/CARLA	OFFER DISCOUNT	DO NOT OFFER DISCOUNT
OFFER DISCOUNT	200 , 500	800 , 300
DO NOT OFFER DISCOUNT	100 , 1000	600 , 700

b) If Carla offers discount, then Sam will choose to offer discount as it gives him a higher pay-off of 200 as compared to 100.

If Carla does not offer discount, then Sam will choose to offer discount as it gives him a higher pay-off of 800 as compared to 700.

So, no matter what Carla chooses, Sam always chooses to offer discount, So, Offering discount is the dominant strategy for Sam.

c) If Sam offers discount, then Carla will choose to offer discount as it gives him a higher pay-off of 500 as compared to 300.

If Sam does not offer discount, then Carla will choose to offer discount as it gives him a higher pay-off of 1000 as compared to 700.

No matter what Sam chooses, Carla always chooses to offer discount. So, offering a discount is the dominant strategy for Carla.

d) If Carla offers discount, then Sam will choose to offer discount as it gives him a higher pay-off of 200 as compared to 100.

If Carla does not offer discount, then Sam will choose to offer discount as it gives him a higher pay-off of 800 as compared to 700.

If Sam offers discount, then Carla will choose to offer discount as it gives him a higher pay-off of 500 as compared to 300.

If Sam does not offer discount, then Carla will choose to offer discount as it gives him a higher pay-off of 1000 as compared to 700.

According to the explanation above, (200 , 500) is the nash equilibrium which means that (offer discount , offer discount) is the nash equilibrium.