The payoff matrix above shows the profits of two firms, Alpha and Beta, that compete against each other. Each firm must decide to set a high or low price. The first numeric entry shows Alpha’s profits; the second entry shows Beta’s profits. Each firm is aware of the information in this payoff matrix.

Nash equilibrium occurs with which combination of strategies?

Question

The payoff matrix above shows the profits of two firms, Alpha and Beta, that compete against each other. Each firm must decide to set a high or low price. The first numeric entry shows Alpha’s profits; the second entry shows Beta’s profits. Each firm is aware of the information in this payoff matrix.

Nash equilibrium occurs with which combination of strategies?

BlackTom AI · Accepted Answer

To analyze Nash equilibrium, we examine each player's best response to the other player's possible actions.
Option 1: Alpha high and Beta low. If Beta chooses low, Alpha’s payoffs are 120 (high) vs 180 (low). Therefore Alpha would prefer low, making High an unlikely best response. This option can’t be a Nash equilibrium because Alpha would deviate to low.
Option 2: Both firms charging a high price. If Beta charges high, Alpha gets 150 with high vs 180 with low; Alpha would deviate to low. Hence this is not a Nash equilibrium since Alpha has an incentive to switch to low.
Option 3: There is no equilibrium in this game. Since the payoff structure shows clear best responses for each firm, a stable pair of strategies exists (the intersection of best responses). Therefore this option is incorrect.
Option 4: Both firms charging a low price. If Beta charges low, Alpha’s best response is low (125 with low vs 120 with high). If Alpha charges low, Beta’s best response is also low (125 with low vs 120 with high). Thus neither firm has an incentive to unilaterally deviate, consistent with a Nash equilibrium.
Option 5: Alpha low and Beta high. If Beta is high, Alpha’s best response is low, which matches this option; however, we must also check Beta’s incentive given Alpha low. If Alpha is low, Beta’s payoffs are 120 (high) vs 125 (low); Beta would prefer low, so Beta would deviate from high to low. Therefore this is not a Nash equilibrium.
In summary, evaluating each scenario by comparing each player’s payoff under the alternative actions shows which configurations yield mutual best responses. The structure of the payoff matrix reveals that the combination where both choose low prices satisfies both players’ best responses, while the other configurations fail because at least one player has a profitable deviation.

AP Economics-Hillebrand AP Microeconomics Sem 1 Exam 2025 - Requires Respondus LockDown Browser

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