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Question 1. [15 points] Consider the following variation of the ultimatum game we have seen in class. Two player, Vince and Jules have to split a suitcase with M $ in it. Vince moves first and makes an offer r ( 0, 1). Then Jules takes the suitcase and can burn a fraction & E [0, 1]of all the money in it. Then money are split according to Vince's suggestion. Vince's payoff is (1-x) (1-6) M and Jules is (1 - 6):M. 1. [5 points] Find all SPE of the game 2. [5 points] Suppose now that dollars are indivisible, so x must be a fraction such that the offer made to Jules is an integer number i.e. Xe , #, ...1. Find all SPE of the game. 3. [5 points] Is there any NE in which Vince is indifferent between any of his actions? (Hint: it doesn't have to be subgame perfect)