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QUESTION 13 [8 Marks] Amy and Seth have to bargain about how to divide R250. Amy moves first. making an offer of some portion of the R250 to aeth. Beth then chooses to accept or reject the offered amount. If aeth accepts, the money is divided according to the proposal. If aeth rejects the offer. the amount is reduced by R50. so that there is R200 left. and then Beth gets a turn. making an offer to Amy. If Beth's offer is accepted. the R200 is divided according to Beth's proposal, but if rejected. the amount is again reduced by R50 and it is Amy's turn again to make an offer. This process continues, with the players taking turns to make offers and the other choosing accept or reject. and the amount being reduced each time an offer is rejected. If the amount reaches R0 before any offer is accepted, the game ends, with both players getting nothing. Assume common knowledge of rationality and that a player who is indifferent between accepting and rejecting will always choose reject. Also note that only integer Rand amount offers are allowed {i.e. no cents). 13.1 Explain what is meant by \"common knowledge of rationality\". 13.2 If the game reaches a state where the amount to be divided is R50. what offer will a rational player make? what is the payoff to the player who made the accepted offer? ariefly explain your answer. 13.3 Use backwards induction to determine what offer my should make in the first round (when there is R250 to divide)