Question

In: Economics

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 $400 in profit and Carla earning $800 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 $100 in profit and Carla earning $1,000 in profit.

Fourth: Carla offers discounts, while Sam does not, which will result in Sam earning $60 in profit and Carla earning $700 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.)

Carla Offers Discounts

Carla Does Not Offer Discounts

Sam Offers

Discounts

Sam Does Not Offer Discounts

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.

Solutions

Expert Solution

a)

Carla Offers Discounts Carla Does Not Offer Discounts

Sam Offers Discounts

 $200, $500 $400, $800
Sam Does Not Offer Discounts $60, $700 $100, $1000

b) Given that Carla offer discounts, Sam's best response is to offer discount($200).
Given that Carla does not offer discounts, Sam's best response is to offer discount($400).
So, Sam's dominant strategy is to offer discounts because it is always chosen by Sam irrespective of Carla's strategy.

c) Given that Sam offer discounts, Carls's best response is to not offer discount($800).
Given that Sam does not offer discounts, Carls's best response is to not offer discount($1000).
So, Carla's dominant strategy is to not offer discounts because it is always chosen by Carla irrespective of Sam's strategy.

d) As they both have a dominant strategy so the NE will be (Sam Offers Discounts, Carla Does Not Offer Discounts) = ($400, $800) because their best response occurs simultaneously at this set. This is the dominant strategy equilibrium.

Rahul Sunny answered 2 years ago
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