Based on the payoff matrix shown, which outcome represents a Nash equilibrium in a duopoly where both firms can choose either 'High Price' or 'Low Price' strategies?

• A. Both firms randomly alternate between 'High Price' and 'Low Price' with no stable outcome.
• B. Both firms choose 'Low Price' and neither can improve their payoff by changing strategy unilaterally.
• C. Both firms choose 'High Price', but one firm can increase its profit by switching to 'Low Price'.
• D. One firm chooses 'High Price' while the other chooses 'Low Price', and both can improve their payoff by switching strategies.

Answer: (B)

Verified step by step guidance

1. Understand the concept of a Nash equilibrium: it is a situation where no player can improve their payoff by unilaterally changing their strategy, given the other player's strategy remains fixed.
2. Identify the possible strategy profiles in the duopoly: (High Price, High Price), (High Price, Low Price), (Low Price, High Price), and (Low Price, Low Price).
3. Examine the payoffs for each strategy profile from the payoff matrix, focusing on whether any firm can increase its payoff by changing its own strategy while the other firm's strategy is held constant.
4. Check the profile where both firms choose 'Low Price': verify that neither firm can improve their payoff by switching to 'High Price' alone, confirming that this profile is stable.
5. Confirm that other profiles are not Nash equilibria by showing that at least one firm can improve its payoff by unilaterally changing its strategy, thus making those outcomes unstable.