Question 4 (i)(a)
Dominant strategies in the advertising game
2 marks
- Time to write
- About 4 minutes
Question
Question 4 (i)(a) · 2 marks- Firms A and B each have to decide whether or not to advertise. Their payoffs (profits in million dollars) are given below:
| Firm B: Advertise | Firm B: Does Not Advertise | |
|---|---|---|
| Firm A: Advertise | (4, 4) | (12, 2) |
| Firm A: Does Not Advertise | (2, 12) | (7, 7) |
- Identify the dominant strategy, if there is one, for each firm.
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- (i)–(a)2 items, each marked on its own: give each its share.
Write it in this order
- 1 Firm A's dominant strategy, with the comparison 1 mark 2 min
- 2 Firm B's dominant strategy, with the comparison 1 mark 2 min
Try it first. About 4 minutes for 2 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Meaning. A dominant strategy is a strategy that gives a player a higher payoff than his other strategy whatever the other player chooses. In each cell below, the first figure is Firm A's profit and the second Firm B's (million dollars).
| B: Advertise | B: Does Not Advertise | |
|---|---|---|
| A: Advertise | (4, 4) | (12, 2) |
| A: Does Not Advertise | (2, 12) | (7, 7) |
Firm A. If B advertises, A earns 4 by advertising and 2 by not advertising, so advertising is better. If B does not advertise, A earns 12 by advertising and 7 by not, so advertising is again better. Advertise is Firm A's dominant strategy.
Firm B. If A advertises, B earns 4 by advertising and 2 by not. If A does not advertise, B earns 12 by advertising and 7 by not. Either way advertising pays more: Advertise is Firm B's dominant strategy.
Answer. Both firms have a dominant strategy, and it is the same for both: advertise. (The game is symmetric, so B's comparison mirrors A's.)
Where the 2 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Firm A's dominant strategy, with the comparison | 1 |
| 2 | Firm B's dominant strategy, with the comparison | 1 |
| Total | 2 |
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