Two construction companies, Giant and Sky, bid for the right to build in a field. The possible bids are $ 10 Million, $ 20 Million, $ 30 Million, $ 35 Million and $ 40 Million. The winner is the company with the higher bid. The two companies decide that in the case of a tie (equal bids), Giant is the winner and will get the field. Giant has ordered a survey and, based on the report from the survey, concludes that getting the field for more than $ 35 Million is as bad as not getting it (assume loss), except in case of a tie (assume win). Sky is not aware of this survey. (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?
Two construction companies, Giant and Sky, bid for the right to build in a field. The possible bids are $ 10 Million, $ 20 Million, $ 30 Million, $ 35 Million and $ 40 Million. The winner is the company with the higher bid.
The two companies decide that in the case of a tie (equal bids), Giant is the winner and will get the field.
Giant has ordered a survey and, based on the report from the survey, concludes that getting the field for more than $ 35 Million is as bad as not getting it (assume loss), except in case of a tie (assume win). Sky is not aware of this survey.
(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 Giant in this game.
(e) Produce an appropriate code to solve the linear programming model in part (d).
(f) Solve the game for Giant using the linear programming model and the code you constructed in parts (d) and (e). Interpret your solution.
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