JellyCat99
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Two parties choose their positions on a political spectrum. Political spectrum is modeled as a set of points {1, 2, ..., 98, 99}, where 1 stands for the most left-wing position, and 99 stands for the most right-wing position. Voters are distributed uniformly on this political spectrum, and we will assume that they always vote for a party that is positioned closer to them. That is, a voter, whose favorite political position is 11, will vote for a party at 14, rather than for a party at 15, or at 6. Voters who are at an equal distance from two parties will b e split evenly among them. The parties choose their positions on the political spectrum simultaneously, and they want to maximize the share of their support.
  1. Show that the strategy of locating the party at position 6 is not dominated?
  2. There are weakly dominated strategies. Find one.
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BobBobson
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1. If one player picks position 6 and the other picks 100, who will win, think about how this proves that picking position 6 is not dominated

2. Think about positions which can never win

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1 or 99. For example if you pick 1, and the other player picks x, the other player will win (99-x) + 1 + 1/2(x-1-1) = 100 - x + 1/2(x-2) = 100 - x + 1/2x -1 = 99- 1/2 x points, and you will win 1 + 1/2(x-1-1) = 1+ 1/2 x -1 =1/2 x. 99 - 1/2 x > 1/2 x, when x <= 99.
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