The above figure shows the payoff to two airlines, A and B, of serving a particular route. If the two airlines must decide simultaneously, what is the Nash equilibrium?

Question

BlackTom AI · Accepted Answer

A Nash equilibrium is a pair of strategies in which each player's choice is a best response to the other player's choice.

1) Relevant concepts
- Payoff matrix: each cell gives (B’s payoff on top, A’s payoff on bottom).
- Best response: the action that yields the highest payoff given the other player's action.
- Nash equilibrium: both players are playing best responses simultaneously.

2) Step-by-step reasoning (showing payoffs)
Read the matrix as:
- If A enters and B enters: A = 10, B = -20.
- If A enters and B does not enter: A = 50, B = 0.
- If A does not enter and B enters: A = 0, B = 40.
- If neither enters: A = 0, B = 0.

3) Compute best responses (intermediate comparisons)
- For A:
  - If B enters: Enter → 10 vs Do not → 0. Best response = Enter (10 > 0).
  - If B does not enter: Enter → 50 vs Do not → 0. Best response = Enter (50 > 0).
  → A has a dominant strategy: Enter.

- For B:
  - If A enters: Enter → -20 vs Do not → 0. Best response = Do not enter (0 > -20).
  - If A does not enter: Enter → 40 vs Do not → 0. Best response = Enter (40 > 0).
  → B’s best response depends on A’s action.

4) Why the correct answer is correct
Because A’s dominant strategy is Enter and when A enters, B’s best response is Do not enter, the profile (A enters, B does not enter) consists of mutual best responses. A would not want to deviate (50 > 0) and B would not want to deviate (0 > -20), so this profile is a Nash equilibrium.

5) Why other options are incorrect
- Both enter: B would deviate to Do not enter (0 > -20), so not a Nash equilibrium.
- Both do not enter: A would deviate to Enter (50 > 0), so not a Nash equilibrium.
- A does not enter but B enters: A would deviate to Enter (10 > 0), so not a Nash equilibrium.

6) Conclusion
The Nash equilibrium is: Firm A enters but Firm B does not enter. This matches the provided answer.

The above figure shows the payoff to two airlines, A and B, of serving a particular route. If the two airlines must decide simultaneously, what is the Nash equilibrium?单项选择题

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