CAMPAIGN STRATEGIES Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson will get
a. Construct the payoff matrix for the game, and show that it is not strictly determined.
b. Find the optimal strategy for both Robinson and Carson.
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Chapter 9 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
- Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 70% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 55% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 20% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 35% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson Robinson P = City Is the game strictly determined? Yes No Q= Rural City (b) Find the optimal strategy for both Robinson (row) and Carson (column). Ruralarrow_forwardBella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 40% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 65% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson City Rural Robinson CityRural Is the game strictly determined? YesNo (b) Find the optimal strategy for both Robinson (row) and Carson (column). P = Q =arrow_forwardTwo mining companies, Red and Blue, bid for the right to drill a field. The possible bids are $ 15 Million, $ 25 Million, $ 35 Million, $ 45 Million and $ 50 Million. The winner is the company with the higher bid. The two companies decide that in the case of a tie (equal bids), Red is the winner and will get the field. Company Red has ordered a geological survey and, based on the report from the survey, concludes that getting the field for more than $ 45 Million is as bad as not getting it (assume loss), except in case of a tie (assume win). (a) State reasons why/how this game can be described as a two-players-zero-sum game (b) Considering all possible combinations of bids, formulate the payoff matrix for the game. (c) Explain what is a saddle point. Verify: does the game have a saddle point? (d) Construct a linear programming model for Company Blue in this game.(e) Produce an appropriate code to solve the linear programming model in part. (f) Solve the game for Blue using the linear…arrow_forward
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