In the following duopoly game, the two firms can either set the price of their product high or low. For each firm, the final profit depends on the price they set as well as the price the other firm sets. The game is represented in the table below.

What is the profit firm A will earn if it plays its dominant strategy:

Question

In the following duopoly game, the two firms can either set the price of their product high or low. For each firm, the final profit depends on the price they set as well as the price the other firm sets. The game is represented in the table below.

What is the profit firm A will earn if it plays its dominant strategy:

BlackTom AI · Accepted Answer

To approach the problem, I’ll lay out the payoff scenarios for Firm A based on its and Firm B’s price choices.
Option 1 (A high, B high) yields A = 1000 and B = 1000. This is one data point for comparing strategies.
Option 2 (A high, B low) yields A = 1500 and B = 800. Here A benefits from choosing a high price when B chooses a low price.
Option 3 (A low, B high) yields A = 800 and B = 1500. This shows A doing poorly when it chooses low while B is high.
Option 4 (A low, B low) yields A = 1250 and B = 1250. In this case, A’s payoff is 1250 with both choosing low.

Now, to identify a dominant strategy for Firm A, compare A’s payoffs from choosing high vs low across both possible prices of Firm B.
- If Firm B chooses High: A would get 1000 with High vs 800 with Low. High is better here.
- If Firm B chooses Low: A would get 1500 with High vs 1250 with Low. Again, High is better here.
Since High Price yields a higher payoff for Firm A regardless of Firm B’s action, High Price is Firm A’s dominant strategy.

Therefore, when Firm A plays its dominant strategy (High Price), the corresponding payoffs are:
- If B is High: A earns 1000.
- If B is Low: A earns 1500.
Among the provided options, the statement that matches this outcome is: "$1000 if firm B has a high price and $1500 if firm B has a low price".

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