A box containing 2 silver buttons is up for sale. Emma and Peili are the only...

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A box containing 2 silver buttons is up for sale. Emma and Peili are the only two interested parties. Emma attaches a value of 3 to each button (so her value for the box is 6), whereas Peili thinks each button is worth 5 (so his value for the box is 10). The (quirky) owner of the button wants to use the following protocol for selling: he asks Emma and Peili to each write down 0, 2 or 4 in a piece of paper and submit it to him. . If they write down the same number, they each get a button and each pay exactly one half of what they write down: so if Emma wrote 2 and Peili wrote 2, Emma's profit will be 3-1 = 2 and Peili's profit is 5-1 = 4. • Otherwise, whoever wrote down the larger number gets both buttons and pay what they wrote down; the other person gets nothing and pays nothing. (a) Write down the matrix representation of this game. (b) Does Emma have a strictly dominated strategy? What about Peili? (c) If you iteratively eliminate strictly dominated strategies, which strategies survive? (d) Going back to the original game in part (a), write down all strategies that form a Nash equilibrium. Justify your answer. A box containing 2 silver buttons is up for sale. Emma and Peili are the only two interested parties. Emma attaches a value of 3 to each button (so her value for the box is 6), whereas Peili thinks each button is worth 5 (so his value for the box is 10). The (quirky) owner of the button wants to use the following protocol for selling: he asks Emma and Peili to each write down 0, 2 or 4 in a piece of paper and submit it to him. . If they write down the same number, they each get a button and each pay exactly one half of what they write down: so if Emma wrote 2 and Peili wrote 2, Emma's profit will be 3-1 = 2 and Peili's profit is 5-1 = 4. • Otherwise, whoever wrote down the larger number gets both buttons and pay what they wrote down; the other person gets nothing and pays nothing. (a) Write down the matrix representation of this game. (b) Does Emma have a strictly dominated strategy? What about Peili? (c) If you iteratively eliminate strictly dominated strategies, which strategies survive? (d) Going back to the original game in part (a), write down all strategies that form a Nash equilibrium. Justify your answer.