Question

Question 2

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 $1000 in profit and Carla earning $800 in profit.

Second: Sam and Carla both offer discounts, which will result in Sam earning $600 in profit and Carla earning $300 in profit.

Third: Sam and Carla both do not offer discounts, which will result in Sam earning $1400 in profit and Carla earning $1000 in profit.

Fourth: Carla offers discounts, while Sam does not, which will result in Sam earning $800 in profit and Carla earning $600 in profit.

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

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

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

Answer 1

Given the above description, we can present it in the following form:

		CARLA
		Discount	No discount
SAM	Discount	(600,300)	(1000,800)
	No discount	(800,600)	(1400,1000)

(A)

Given the above payoff matrix, it is clear that Sam earns a higher payoff by offering "No discount" irrespective of what Carla chooses. Hence, Sam's dominant strategy is - NO DISCOUNT.

(B)

From the above payoff matrix, it can be seen that Carla also earns a higher payoff by offering "No discount' irrespective of whether Sam offers a discount or not. Hence, Carla's dominant strategy is - NO DISCOUNT.

(C)

Since both Sam and Carla have a dominant strategy of "No Discount", hence the Nash equilibrium to the above game is - (No Discount, No Discount) with a payoff of (1400,1000) for Sam and Carla respectively. This is because both will simultaneously choose their optimal strategies and will thus earn a higher payoff.