Need assistance constructing and analyzing game trees from payoff matrices.
Need assistance constructing and analyzing game trees from payoff matrices.
Need assistance constructing and analyzing game trees from payoff matrices.Need assistance constructing and analyzing game trees from payoff matrices.
Instructions
A telecom company is considering upgrading their infrastructure in your city and they have hired G&B consulting to help them determine their optimum strategy. The telecom company would be willing to invest in upgraded lines that offer higher speeds and bandwidth, but it is costly to do so and they are afraid they might make the investment but not have customers willing to upgrade their services which would be needed to recoup their profits. The alternative would be to keep the old infrastructure, but there are already a high amount of service complaints from the customer base. The telecom company needs to determine if investing in the improved service will pay off for them by having a sufficient amount of customers buy the upgraded service.
The market research team working on the project creates this payoff matrix that represents the scaled values that customers give to the different levels of service and payouts for the telecom company:
|
|
Telecom Company |
||
|
|
Upgrade |
Don’t Upgrade |
|
|
Customers |
Buy |
(2, 2) |
(0, 3) |
|
Don’t Buy |
(1, 0) |
(1, 1) |
|
You recognize that this is not a simultaneous game, and the payoff matrix is not the best form of analysis. Construct a game tree to model this scenario. Compose an email to your coworker to explain why a game tree should be used instead of this payoff matrix, and make a note of any cells that should be excluded.
Perform backward induction on the game tree to find the optimum strategy.
Show all work, including any payoff matrices and game trees used, all steps of backwards induction, and any necessary explanations with your solutions.
