ECON 106G Lecture 3: 106G Lecture Note 3-16

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28 May 2016
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Each student chooses a number between 1 and 100. 2/3 of the average of the chosen numbers wins the game. (cid:15) i: 106g students (cid:15) si = f1; (cid:1) (cid:1) (cid:1) ; 100g (cid:15) ui (si; sj) = (cid:0)(cid:12)(cid:12)si (cid:0) 2. One could start with the belief that the other students randomize over the numbers. Then the average is 50 and 2/3 of that is 33. If one believes that all of the others are picking 100, 2/3 of the average is 67. If one believes that all of the other players are picking 1, the best response is to pick 1 oneself. Thus, all strategies si = 1; :::; 67 are best responses, but all strategies s0 i = 68; :::; 100 are strictly dominated by si = 67. ui (s0 i; sj) = (cid:0)(cid:12)(cid:12)(cid:12)(cid:12)s0 i (cid:0) 3 s(cid:12)(cid:12)(cid:12)(cid:12) = (cid:0) js0 i (cid:0) 67j (cid:0) (cid:12)(cid:12)(cid:12)(cid:12)67 (cid:0)

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