Recent developments in a particular marketing district resulted in the determination of three areas: X, Y...

 

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Recent developments in a particular marketing district resulted in the determination of three areas: X, Y and Z. The location of these areas and the number of customers expected in each per month are as follows: Y 30.000 6 km. X 25.000 10 km. 8 km. Z 45.000 Two competing companies, D and E, are planning to establish operating branches in the district. The location of the branch is confidential but a market research company provided both companies with the following information: If D is closer to an area, then it captures 75% of the business. If E is closer to an area, D will get only 30% of the business. If D and E open a branch at the same distance from the areas, then market will be shared 55:45 in favor of E. Set up the payoff matrix with E as row. a) Use dominance to reduce the number of strategies for either player. List the order of eliminated strategies. b) If the resulting matrix is 3x3 or larger, derive the LP equations for the game solution (both for row and column); do not solve. c) If the resulting matrix is Nx2 or 2XM use graphical method; if 2X2, use expected value method to solve the game. Recent developments in a particular marketing district resulted in the determination of three areas: X, Y and Z. The location of these areas and the number of customers expected in each per month are as follows: Y 30.000 6 km. X 25.000 10 km. 8 km. Z 45.000 Two competing companies, D and E, are planning to establish operating branches in the district. The location of the branch is confidential but a market research company provided both companies with the following information: If D is closer to an area, then it captures 75% of the business. If E is closer to an area, D will get only 30% of the business. If D and E open a branch at the same distance from the areas, then market will be shared 55:45 in favor of E. Set up the payoff matrix with E as row. a) Use dominance to reduce the number of strategies for either player. List the order of eliminated strategies. b) If the resulting matrix is 3x3 or larger, derive the LP equations for the game solution (both for row and column); do not solve. c) If the resulting matrix is Nx2 or 2XM use graphical method; if 2X2, use expected value method to solve the game.

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