14.123 Microeconomic Theory III, 2010 Final exam with solutions
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Answer: For the preferences to be the same, it must be that vi = aiui+bi for some ai and bi where ai is positive and ui and vi are the utility functions of i in the left and the right game, respectively. Since u1 (b,M) = 0 and v1 (b,M) = 3, we must have b1 = 3 (Row player is 1 and the column player is 2.) Since u1 (c,M) = 1 and v1 (c,M) = 5, we then have a1 = 2. But v1 (a, L) = 12 6 · 2+3 = 2 . = 2 u1 (a, L)+3 Therefore, Player 1’s preferences are different in two games. On the other hand, one can easily see that u2 = 3v2 + 1, showing that the preferences of Player 2 are identical in the two games.
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تاریخ انتشار 2010