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.

The Nash equilibrium for this game is for:

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.

The Nash equilibrium for this game is for:

BlackTom AI · Accepted Answer

We start by restating the scenario and the answer choices to orient the analysis.
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 Nash equilibrium for this game is for:
Answer options:
- both firms to sell the product at a low price
- firm A to sell at a high price and for firm B to sell at a low price
- both firms to sell the product at a high price
- firm A to sell at a low price and for firm B to sell at a high price

Option 1: both firms to sell the product at a low price.
- If both choose Low, the payoffs are 1250 for Firm A and 1250 for Firm B according to the table. To judge whether this is a Nash equilibrium, we need to see if either firm has an incentive to deviate unilaterally. Consider Firm A: if Firm B stays at Low, Firm A’s best response is to switch to High because 1500 (High price when B is Low) > 1250 (Low price when B is Low). Therefore, Firm A would deviate from Low to High, so (Low, Low) is not a Nash equilibrium. The same logic applies symmetrically for Firm B. This option is not a stable outcome because each firm can improve its payoff by unilaterally changing to High when the other stays at Low.

Option 2: firm A high, firm B low.
- The payoff for (High, Low) is (1500 for A, 800 for B). If Firm B anticipates this, could B do better by switching to High? When A is High, B’s payoff with High would be 1000 (from (High, High)) rather than 800, so B would prefer to switch to High. Thus (High, Low) is not a Nash equilibrium since B has an incentive to deviate to High. Likewise, A’s position could be evaluated, but the key point is that at least one firm has an incentive to deviate, so this is not a Nash equilibrium.

Option 3: both firms to sell the product at a high price.
- The payoff is (1000 for A, 1000 for B). To check if this is a Nash equilibrium, examine whether either firm can improve by deviating unilaterally. If Firm B expects A to stay at High, B’s payoff from switching to Low would be 800, which is worse than 1000, so B has no incentive to deviate. If Firm A expects B to stay at High, A’s payoff from switching to Low would be 800, which is worse than 1000, so A also has no incentive to deviate. Therefore, (High, High) is a stable outcome where neither firm benefits from unilateral deviation, satisfying the Nash equilibrium condition.

Option 4: firm A low, firm B high.
- The payoff is (800 for A, 1500 for B). If Firm A anticipates B is High, A’s alternative when switching to High would yield 1000 (since (High, High) gives A 1000) which is greater than 800. Thus A would deviate to High, so (Low, High) is not a Nash equilibrium. Similarly, if A stayed Low, B could consider deviating, but the critical point is A’s incentive to switch makes this profile unstable.

Summary of the per-option analysis:
- Low-Low: not an equilibrium because each firm can gain by moving to High.
- High-Low: not an equilibrium because the Low-priced firm (B) would prefer to move to High when A is High.
- High-High: appears to be a Nash equilibrium since neither firm can improve by unilateral deviation given the other’s High pricing.
- Low-High: not an equilibrium because the Low-priced firm (A) would move to High when B is High.

Note: In this analysis we follow the payoff structure shown in the table to identify best responses and check for mutual best replies. The outcome where both firms set a High Price (High, High) yields equal payoffs of 1000 each and satisfies the condition that neither firm can improve their payoff by deviating alone.

23566 Economics for Business 2 - Spring 2025 🔴 Quiz 3 - Monopolistic competition and Oligopoly

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. The Nash equilibrium for this game is for:

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