Refer to the normal-form game of price competition shown below. Firm B is the incumbent facing potential entry from its rival, firm A. Firm A's strategies consist of {entry, stay out}. Firm B's strategies are then {hard if entry; hard if stay out; soft if entry; soft if stay out}. Find the subgame Nash equilibrium to this game, if one exists.
A) Firm A plays {stay out}; firm B plays {hard if entry}.
B) Firm A plays {entry}; firm B plays {hard if entry}.
C) Firm A plays {entry}; firm B plays {soft if entry}.
D) There is no subgame Nash equilibrium to this game.

Question

Refer to the normal-form game of price competition shown below.  Firm B is the incumbent facing potential entry from its rival, firm A. Firm A's strategies consist of {entry, stay out}. Firm B's strategies are then {hard if entry; hard if stay out; soft if entry; soft if stay out}. Find the subgame Nash equilibrium to this game, if one exists.
A) Firm A plays {stay out}; firm B plays {hard if entry}. 
B) Firm A plays {entry}; firm B plays {hard if entry}. 
C) Firm A plays {entry}; firm B plays {soft if entry}. 
D) There is no subgame Nash equilibrium to this game.

Quizplus · Accepted Answer

To find the subgame Nash equilibrium, we must first identify the subgame. In this case, it is the second stage of the game, where Firm B chooses its pricing strategy.

If Firm A enters, Firm B will choose to play hard regardless of whether A stays out or enters. Therefore, if Firm A enters, there is no subgame Nash equilibrium because Firm A is indifferent between its two strategies and Firm B's strategy is not a best response to either of A's strategies.

However, if Firm A stays out, Firm B's best response is to play soft. This leads to a unique subgame Nash equilibrium, where Firm A stays out and Firm B plays soft if entry. Therefore, the answer is C, Firm A plays {entry}; firm B plays {soft if entry}.

Refer to the Normal-Form Game of Price Competition Shown Below