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 a e [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-r)(1-6)M and Jules is (1-8)aM. 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)