Question

John and Anne are the only two suppliers of snacks at school while everyone waits for a ride after sports and clubs. Each student can choose to set a high price or a low price for their goods. The payoff matrix below shows the daily profits for each combination of prices that John and Anne could set. The first entry shows Anne's profits, and the second entry shows John's profits. Assume that both students know the information shown in the matrix. Study the matrix, and then answer the questions that follow.

Do John and Anne each have a dominant strategy to set a high price, a dominant strategy to set a low price, or no dominant strategy?

Anne

John

If John and Anne do not cooperate on price setting, what will be the profit for each of them?

Anne

John

A club sponsor with hungry students agrees to pay $4 to John and Anne each if they charge the lower price for their snacks. Redraw the payoff matrix with this subsidy

John High Price Low Price Anne High Price Low Price $21, $22 $24, $16 $8, $26 $15, $14

Answer 1

a) Given the above payoff matrix for John and Anne, Anne's dominant strategy is to charge high prices. This is because when John charges high prices, anne earns more by charging high prices and when John charges low prices, Anne still earns more by charging high prices.

Thus, Anne's dominant startegy = High prices

In the case of John, when anne charges high prices, John earns more by charging low prices and when Anne charges low prices, John earns more profit by charging high prices.

Clearly, John does not have a dominant strategy.

b) If John and Anne do not cooperate in setting prices, the equilibrium outcome will be - (Low price, high price) with a payoff of (24,16) for Anne and John respectively.

c) Given thatthe club offers $4 to each John and anne in order to charge low prices, the new payoff matrix will be given as:

		John
Anne		High price	Low price
	High price	21, 22	8,30
	Low price	28,16	19, 18