Currently Sam and Carla have the only taxi services in a small town. Both Sam and...
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 $500 in profit and Carla earning $600 in profit.
Second: Sam and Carla both offer discounts, which will result in Sam earning $300 in profit and Carla earning $800 in profit.
Third: Sam and Carla both do not offer discounts, which will result in Sam earning $800 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.
Homework Answers
a) The pay-off matrix for the above game is constructed as follows where the first number is the pay-off for Sam and second number if the pay-off for Carla:
| SAM / CARLA | OFFER DISCOUNT | OFFER NO DISCOUNT |
| OFFER DISCOUNT | 300 , 800 | 500 , 600 |
| OFFER NO DISCOUNT | 100 , 1000 | 800 , 700 |
b) If Carla chooses to offer a discount, then Sam will choose to offer a discount as it gives him a higher pay-off of 300 as compared to 100.
If Carla chooses to not offer a discount, then Sam will choose to not offer a discount as it gives him a higher pay-off of 800 as compared to 500.
So, Sam does not have any dominant strategy as every time Carla changes his/her strategy, Sam also changes his/her strategy.
c) If Sam choose to offer a discount, then Carla will choose to offer a discount as it gives him a higher pay-off of 800 as compared to 600.
If Sam chooses not to offer a discount, then Carla will choose to offer a discount as it gives him a higher pay-off of 1000 as compared to 700.
So, Carla has a dominant strategy of choosing to offer a discount no matter what strategy Sam adopts.
d) From the above explanation in part b and part c, the nash equilibrium is (300 , 800) that is (offer discount, offer discount) that is nash equilibrium is when both the players offer a discount.
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