I could solve Question 25 (simultaneous location game between 2 firms), but I'm confused between options b) and d) for Question 26 (sequential game involving a third firm). I have attached both questions since Question 25 provides context to Question 26. Basically, I got my answer as d) for Question 26, using the method of backward induction since it's a sequential game. While the answer key for this question says b) is the correct option. My method: Assuming that firm 3 locates at 1/2, firm 1 and 2's location described in option d) gives them both the maximum share than in any other option. Equilibrium should be such that firms 1 & 2 are at an advantage since they are first movers in the game.
Could anyone please confirm as to which should be the correct option for Question 26? Any solution and views are welcome.