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

Firm A prefers to enter the market than staying out as long as its profit from entry (10 units) is greater than the profit from staying out (0 units). Firm B, being the incumbent, would always prefer a soft strategy over a hard strategy. Thus, Firm B would choose the soft strategy if Firm A enters and the hard strategy if Firm A stays out. This results in a unique subgame Nash equilibrium where Firm A plays {entry} and Firm B plays {soft if entry}.

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