Consider the game given above. (a) How many histories are in the game? (b) How many sub games are there? (c) How many strategies does player 1 have? Calculate this number. (d) Solve for the sub game perfect equilibrium using backward induction. Indicate in the game tree all the sub game perfect equilibrium strategies of each player by drawing for each history a line parallel to the edge representing the action that the player chooses at this history.