problemset1_2012_solutions

# problemset1_2012_solutions - Game Theory and Strategy...

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Game Theory and Strategy ECON-UA 216 Solutions to Problem Set 1 1 Strictly and weakly dominated strategies Here is an example of a two-player game matrix where Player 2’s strategy l is strictly dominated by both strategies c and r , while Player 1’s strategy M weakly dominates U. l c r U 2,1 2,3 5,2 M 3,2 3,3 5,4 D 4,0 1,5 2,6 2 Iterative deletion of dominated strategies Part A l c r U 1,1 0,1 3,1 M 1,0 2,2 1,3 D 1,3 3,1 2,2 The game has no strictly dominated strategy. Strategy r for Player 2 weakly dominates c , while for Player 1 notice that D weakly dominates M. Part B We ﬁrst delete strategies c and M and then notice that in the reduced game below r and D are weakly dominated. l r U 1,1 3,1 D 1,3 2,2 The outcome given by Iterated Deletion of Weakly Dominated Strategies is { U,l } . 1

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Game Theory Solutions to P. Set 1 Part C Notice that the problem with this NE outcome is that : intuitively, Player 2 is indiﬀerent between l,c,r when Player 1 plays U . If Player 2 switches to c, in which case Player 1 is left with a zero payoﬀ. 3 Hotelling’s location game Part A First notice that when he plays strategy 1 and his opponent picks any other pure strategy s 2 6 = 1, Player 1 gets a payoﬀ π 1 = 10 s 2 2 (when s 2 = 1, they both get 50). The easiest way to get the answer is, as the text suggest, to guess and verify. In particular, a good strategy is to try to imagine what the worst case is.
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problemset1_2012_solutions - Game Theory and Strategy...

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