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There are n firms considering the acquisition of a target business activity. They move in sequence. If Firm 1 does not acquire the target, the opportunity is gone and the game ends. If Firm 1 acquires the target, it becomes itself a target for an acquisition, and Firm 2 can then acquire it. If Firm 2 chooses not to acquire Firm 1, the game ends. If Firm 2 acquires Firm 1, then Firm 2 may be in turn acquired by Firm 3, and so on. The preferred outcome for each firm (with a payoff of 2) is to acquire the business activity or another firm) and not be acquired (by another firm), the second preferred is not to acquire (payoff of 1), and the worst outcome is to be acquired by another firm (payoff of 0). There are n firms in total. (a) [10 marks] Use the graphical tree representation to describe the extensive form of the game with n=3 firms. [10 marks] For n=3, find a subgame perfect equilibrium of the game described. Carefully describe the equilibrium strategies of all the 3 firms. (©) [10 marks] Find a Nash equilibrium of the game described (with n=3) that is not subgame perfect equilibrium. Describe the equilibrium strategies of the three players in this equilibrium. a (d) [10 marks] For n=2, identify the unique subgame-perfect equilibrium and all pure strategy Nash equilibria. (e) [10 marks] Would the choice of firm I be different (from what you found in (b)) in a subgame perfect equilibrium when there are n=4 firms? And when there are n=5 firms? Properly motivate your answer.