$ 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 programming model and the code you con- structed in parts (d) and (e). Interpret your solution.
Two 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 programming model and the code you con- structed in parts (d) and (e). Interpret your solution.
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