Question

1. Basic Game Theory (21 points) Consider the following game Player Top Bottom Left 21, 23 22. 16 Player 2 Right 20, 24 19. 18 A. (6 points) Does player 2 have a dominant strategy. If yes, describe it B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff matrix, find the Nash equilibrium for the new game below: Player 2 Left Right Player 1 Top 21, 28 28, 27 Bottom | 19,25 29.26 2. Price Discrimination (24 points) First indicate the types of price discrimination for the cases below. Then explain the differences between the different types of price discrimination that you find in these examples. Case A: Pop singer XXX is announcing a concert tour starting next summer, and there is a 20% price discount for those loyal fans who have always been actively participating in XXX's official fan club in the last two years. Since Chase Bank is a big sponsor of this tour, anyone using the Chase Freedom credit card to buy the ticket can enjoy a 10% discount. Moreover anyone who buys the ticket can enjoy a 10% discount when they also shop at XXX's online merchandise store. Case B: At ABC Yoga studio the price of a single yoga class is $18, a five-class yoga pass (expires in two months) costs $80, and a ten-class pass (expires in four months) costs $150. It also offers the weekday morning class special discount: one month of unlimited weekday classes before 2pm at S109.99 (one month of unlimited class is at $139.99.) Moreover it offers veterans and senior citizens a 10% discount to all classes. 3. Cournot Competition (26 points) Consider a Cournot model. The market demand is p=120-91-92. Firm l's marginal cost is 30, and firm 2's marginal cost is also 30. There are no fixed costs. A. (10 points) Derive the best response function for each firm. B. (6 points) Find the Nash Equilibrium.

Answer 1

Dominant strategy refers to that strategy followed by one of the players in the game regardless of the strategy what the other player has adopted.

a)

Represent the table as follows:

Player 1	Player 2
			C	D
	Top		Left	Right
	Bottom	A	21,23	20,24
		B	22,16	19,18

Yes, player 2 has a dominant strategy C. (As player 2 gets higher pay off from strategy C).

b)

Yes, the game can be solved by elimination of dominated strategy.

If Strategy D for player 2 is eliminated, then the game is :

                                                                             Player 2

Player 1		C
	A	21,23
	B	22,16

Thus, the Nash equilibrium by eliminating dominated strategy is (A,C). (As row B is dominated by row, so it is eliminated).

c)

Represent the table as follows:

Player 1	Player 2
			C	D
	Top		Left	Right
	Bottom	A	21,28	28,27
		B	19,25	29,26

Thus, the Nash equilibrium is: (B,C) and (A,D).