Question

1. (30 points) There are two firms considering introducing a new product to the market. Each firm can either set a high price or low price for its product. If both set a low price the market will be shared between the two firms. In this case, each firm expects to make a profit of $2m. If one firm sets a high price while the other sets a low price, the former is expected to make $1m and the latter is expected to make $5m. When both set a high price, again, the market will be shared and each firm expects to make a profit of $4m. If both firms know all this information and will choose their prices simultaneously, without knowing what the other chooses, what will be the outcome? What price would each firm pick?

Answer 1

Answer

Lets first form a payoff table

According to above information we have a following Payoff Table:

Payer 2

		Low	High
Player 1	Low	2 m , 2 million	5 m , 1 m
	High	1 m , 5 m	4 m , 4 m

Suppose Player 1 thinks that Player 2 will choose Low then Player 1 will also decide to choose Low because it will get higher profit if it chooses Low

Also, If Player 1 thinks that Player 2 will choose Low then we can see from above payoff table Player 1 will also choose Low because it will give him higher profit if it chooses Low.

Hence Player 1 will always choose Low. Hence Low is a dominant strategy of Player 1

Similarly,

Suppose Player 2 thinks that Player 1 will choose Low then Player 2 will also decide to choose Low because it will get higher profit if it chooses Low

Also, If Player 2 thinks that Player 1 will choose Low then we can see from above payoff table Player 2 will also choose Low because it will give him higher profit if it chooses Low.

Hence Player 2 will always choose Low. Hence Low is a dominant strategy of Player 2

Hence Both will choose Low and each will earn profit of 2 million.

So, Each Firm will choose Low Price and each firm will earn profit of $2 m