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{"ops":[{"insert":"Consider the following voting game. There are three players, 1, 2 and 3. And there are three alternatives: A, B and C. Players vote simultaneously for an alternative. Abstaining is not allowed. Thus, the strategy space for each player is {A, B, C}. The alternative with the most votes wins. If no alternative receives a majority, then alternative A is selected. Denote ui(d) the utility obtained by player i if alternative d \ud835\udf16\u00a0\u00a0\u00a0{A, B, C} is selected.\u00a0\nThe payoff functions are,\u00a0\nu1(A) = u2(B) = u3(C) = 2\u00a0\nu1(B) = u2(C) = u3(A) = 1\u00a0\nu1(C) = u2(A) = u3(B) = 0\u00a0\u00a0\na. Let us denote by (i, j, k) a profile of pure strategies where player 1\u2019s strategy is (to vote for) i, player 2\u2019s strategy is j and player 3\u2019s strategy is k. Show that the pure strategy profiles (A,A,A) and (A,B,A) are both Nash equilibrium.\u00a0\u00a0\nb. Is (A,A,B) a Nash equilibrium? Comment.\u00a0\u00a0\n"}]}
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