Consider the situation in which Player M is an INCUMBENT monopolist in an industry, which makes a profit of $10m if left to enjoy its privileged position undisturbed. Player P is a firm that could (POTENTIALLY) Enter the market (E), or Stay out (S); if it chooses not to enter its residual activities outside of the market make a profit of just £2m. If the potential entrant, P, decides to enter then the monopolist, M, can do one of two things: it can Fight (F) by flooding the market with its product so as to force down the price, or it can Acquiesce (A) and split the market with the entrant. A fight is damaging to both M and P and as a consequence they both make zero profits (£0m). If they split the market, each will each make a profit of £4m.
Denote the strategy set for P as {E, S} and that for M as {A, F} : Find the perfect sub game Nash Equilibrium, typing your answer as either (S), (E,A) or (E, F) ; but remember the brackets, commas, upper case letters, AND no spaces.