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Assignment 4

# Assignment 4 - general idea is that Bill should swat the...

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Economics 146 – Fall, 2007 Homework Assignment 4 – due December 6, 2007 Last update: 11/28/07 Reminder for problems 2 and 3: a pure strategy is a complete instruction set for what a player should do at every possible contingency he might encounter in a play of the game. 1. By means of the “streamlined” transportation algorithm find a solution for the trans- portation problem given by the cost/supply/demand matrix: 1 2 3 4 1 10 5 6 7 28 2 8 2 7 6 25 3 9 3 4 8 47 15 20 30 35 Here, the entries of the left-most column are the index numbers of the plants(sources), and the entries of the top-most row are the index number of the markets(destinations). The entries of the right-most column are the supplies at the three plants, and the entries of the bottom-most row are the demands at the four markets. The entries in the matrix proper are transportation costs: c ij is the cost to transport one unit of the of the commodity from plant i to market j . 2. Al and Bill play a game. Al has a real fly and a fake fly. Bill has a fly-swatter. The
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Unformatted text preview: general idea is that Bill should swat the real ﬂy. Al chooses the real ﬂy or the fake ﬂy, puts it on the table and conceals it with his hand. Meanwhile Bill decides whether or not he will swat the ﬂy. At a signal Al removes his hand and Bill swats or not. If Bill swats he wins one dollar if the ﬂy was real and loses one dollar if the ﬂy was fake. If Bill does not swat and the ﬂy was real, there is no payment and the game ends because the ﬂy ﬂies oﬀ. If Bill does not swat and the ﬂy was fake, they play the game once more – this time for double stakes, and this time if Bill does not swat the fake ﬂy Bill wins two dollars and the game ends. Make Al player I. (a) List the pure strategies for each player and give the payoﬀ matrix. (b) Find a solution for this game. 3. Solve the following matrix game parametrically. Give the solutions as a function of t. " 0 2 t 1 #...
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