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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 x ? [0, 1]. Then Jules takes the suitcase and can burn a fraction ? ? [0, 1]of all the money in it. Then money are split according to Vince's suggestion. Vince's payoff is (1 ? x)?M and Jules is ?xM.

1. [5 points] Find all SPE of the game
2. [5 points] Suppose now that dollars are indivisible, so x must be an integer number ? 1, 2, ...M . 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)

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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 x E [0, 1]. Then Jules takes the suitcase and can burn a fraction o E [0, 1]of all the money in it. Then money are split according to Vince's suggestion. Vince's payoff is (1 - x)6M and Jules is SxM. 1. [5 points] Find all SPE of the game 2. [5 points] Suppose now that dollars are indivisible, so x must be an integer number E 1, 2, ...M. 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)