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There are two firms who compete simultaneously and independently by selecting prices for their goods. Firm...

There are two firms who compete simultaneously and independently by selecting prices for their goods. Firm 1's product and firm 2's product are imperfect substitutes, so that an increase in one firm's price will lead to an increase in the quantity demanded of the other firm's product. In particular, each firm i faces the following demand curve given firm j's price: qi = max {0, 36 – 2pi + pj } Here qi is the quantity sold by firm i, pi is firm i's price, and pj is firm j's price. The “max” operator guarantees quantities cannot be negative. Suppose the maximum price is 20 and the minimum price is 0 for both firms, and there are not costs.

1. What is the best response function for each firm?

2. What is the set of undominated strategies for each firm (that is, under rationality, but not requiring the common knowledge of rationality)?

3. What is the rationalizable set of strategies for each firm?

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Answer #1

(1) J's firm best response function due to increase of quantity.

i's response decrease due to increase of price and quantity decreases.

(2).The price is dominating the demand of the product. The product is depend upon the price only then the demand increase.

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