6. On a warm day in May, a group of five Warwick students (in order of age A, B, C, D and E with A the oldest) decide to go for a walk on campus to take a break from revising for their EC202 exam. They enter a fairly secluded part of campus and by accident, they discover a hidden box containing 1000. They must now decide how to distribute it between them and they agree on the following rules. The oldest student first proposes a plan of distribution. The students, including the proposer, then vote on whether to accept the proposal. If the majority accepts the plan, each student receives their share according to the proposal and the game ends. If there is a tie, the proposer has the casting vote. If the majority rejects the plan, the proposer is ostracised (sent to Coventry!), and the second oldest student makes a new proposal to begin the system again. The process is repeated until a plan is accepted or only one student (the youngest) is left. Payoffs are as follows. First, each Warwick student does not want to be ostracised and would receive a payoff equal to -100 (in monetary terms) if this happens. Second, given they're not ostracised, they want to maximise their share of the find. Third, each student prefers to ostracise another (each player receives a small payoff equal to 1 for ostracising one of the other students) if all other results would otherwise be equal. Find an allocation which can be supported as a subgame perfect Nash equilibrium in this game. (Hint: use backwards induction). (28 marks)