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.

My answer is for the firm to enter and to Acquiesce. How about your answer? Please do give your opinion on this, thank you.