Two firms compete against each other. Currently Firm 1 earns? $10 million per year and Firm 2 earns? $13 million. Both expect to earn the same amount in the future if no changes are made. Firm? 1, however, is considering whether to introduce an improved version of its product. If it? does, and if Firm 2 does nothing in? response, Firm? 1's profit will increase to? $13 million and Firm? 2's profit will drop to? $12 million.
Instead of doing nothing in response to Firm? 1's improved? product, Firm 2 could respond by increasing its advertising budget. If it does? so, and if Firm 1 does not? retaliate, Firm? 1's profit will be? $10 million and Firm? 2's profit will be? $12 million.
?Finally, if Firm 2 increases its advertising budget and Firm 1 retaliates by raising its advertising? budget, Firm 1 will earn? $12 million and Firm 2 will make? $11 million.
To solve this sequential? game, work backward from the end to determine each? firm's optimal action at each stage of the game. Both firms are? rational, fully? informed, and want to maximize their profits. You may find it useful to write out the game in extensive form.
The solution to the game is a sequence of moves by the two firms. For? example, Firm 1 could do nothing and that would be the end of the game. Or Firm 1 could introduce the new product? version, Firm 2 could increase its advertising? budget, and Firm 1 could then increase its advertising budget in retaliation. There are also two other possible sequences.
The solution to this game is the following sequence of actions by the two? firms:
A. Firm 1 does not introduce the new product version.
B. Firm 1 introduces the new product version and Firm 2 does not increase its advertising budget.
C. Firm 1 introduces the new product? version, Firm 2 increases its advertising? budget, and Firm 1 does not retaliate.
D. Firm 1 introduces the new product? version, Firm 2 increases its advertising? budget, and Firm 1 retaliates by raising its advertising budget.