It's a GameTheory question from past exams, need help with it.

Consider an industry with two rms: an incumbent (player 1) and a potential entrant [player 2}. Player 1 decides whether to build a new plant, and simultaneously player 2 decides whether to enter. hnagine that player 2 is uncertain whether player 1's cost of building is 3 or 1.5, while player 1 knows her cost. Both costs of player 1 are equally likely. The payos are depicted below. 1 f2 (highcost) Build 0 -1 2, 0 Don't build 2,! 0.5 3 1f2 [low-cost) Enter Build 1.5 Don't build 2, [1.5 [a] Formulate this game as a Bayesian game. How many types does each player have? [b] Find all Bayesian Nash equilibria in which player 2 plays a pure strategy. (c) Can the highcost incumbent ever be indifferent between building and not building in a BNE? Find a Bayesian Nash equilibrium in which the entrant and the lowcost incumbent mix