Question

1. The two largest cigarette producers are Phillip Morris and R. J. Reynolds. Both are considering whether to increase their price for a pack of cigarettes or keep the price unchanged.

          The relevant factors to consider are: 1) demand for cigarettes is inelastic, so if both firms raise prices they will increase their revenue, and 2) if one raises price and the other doesn’t, they will lose market share to their rival

                                                R. J. Reynolds

                                       Increase                 No change

                   Increase      R: 500 million           R: 400 million

                                      P: 600 million           P: 300 million

Phillip Morris

                   No change R: 200 million           R: 300 million

                                      P: 500 million           P: 400 million

Does either cigarette maker have a dominant strategy? Why or why not? Use the above matrix to answer, and assume the two companies do not cooperate

         

For purposes of the problem, ignore the existence of other cigarette makers.

2. Does the answer to #1 change if the two firms can cooperate?

3. How would your answer to #1 change if the outcome matrix changed to the following:

                                                R. J. Reynolds

                                     Increase                 No change

                   Increase      R: 400 million           R: 500 million

                                      P: 500 million           P: 300 million

Phillip Morris

                   No change R: 200 million           R: 300 million

                                      P: 600 million           P: 400 million

Answer 1

1. When P choose Increase, R's best response is Increase(500).
When P choose No change, R's best response is No change(300).
Thus, R J Reynolds does not have a dominant strategy because there is no single strategy which is always its best response.

When R choose Increase, P's best response is Increase(600).
When R choose No change, P's best response is No change(400).
Thus, Phillip Morris does not have a dominant strategy because there is no single strategy which is always its best response.

There are two pure strategy Nash equilibria. They are (Increase, Increase) = (R: 500; P: 600), and (No change, No change) = (R: 300; P: 400) because their best response occurs simultaneously at these sets.

2. Even if the two could cooperate, the above outcomes would not change because there are no other outcomes which would make both of them better off simultaneously.

3. When P choose Increase, R's best response is No change(500).
When P choose No change, R's best response is No change(300).
Thus, R J Reynolds' dominant strategy is no change as it is always its best response.

When R choose Increase, P's best response is No change(600).
When R choose No change, P's best response is No change(400).
Thus, Phillips Morris's dominant strategy is no change as it is always its best response.

So, the pure strategy NE is (No change, No change) = (R: 300; P: 400)