# Math Help - Game theory: subgame perfect nash equilibrium

1. ## Game theory: subgame perfect nash equilibrium

Consider the situation, where Player X is incumbent monopolist, which makes profit of $10m if left to enjoy its position undisturbed. Player Y is firm that could potentially ENTER the market (E) or STAY out (S). If Y does not enter, it will get profit of$2m. However If Y decides to enter, then the monopolist A can do two things; Fight (F) or Acquiesce (A). If monopolist X chose to fight, both will make zero profit ($0m). If they choose to split the market, they will each make profit of$4m.
Find the subgame perfect nash equilibrium.

2. I do agree with your answer: to enter and Acquiesce. Taking a look at the Prisoner's Dilemma might help you understand why this is so.

Prisoner's dilemma - Wikipedia, the free encyclopedia