Game Theory and Best Decision
Homework Assignment 1
Decision Analysis
Questions 1-6 refer to the following
A family business is considering making an investment in its manufacturing operation. Three decisions are under consideration: (1) a large investment; (2) a medium investment; and (3) a small investment. The business believes that there are three possible future outcomes for its product: (1) increasing demand; (2) stable demand; and (3) decreasing demand. The following payoff table describes the decision situation.
|States of Nature |
|Decision |Increasing Demand |Stable Demand |Decreasing Demand |
|Large Investment |$1,000,000 |$400,000 |-$600,000 |
|Medium Investment |500,000 |300,000 |-200,000 |
|Small Investment |250,000 |125,000 |25,000 |
1. Identify the best decision using the maximax criterion.
Maximax $1,000,000 $500,000 $250,000
The best decision using the maximax criterion is the large investment of $1,000,000 because it has the most payoff.
2. Identify the best decision using the maximin criterion.
Min -600,000 -200,000 25,000
The best decision using the maximin criterion is the small investment of $25,000.
3. Identify the best decision using the equal likely criterion.
Average $1,000,000 + $400,000 + (-600,000) = 800,000/3= 266,666.666 $500,000 + $300,000 + (-200,000) = 600,000/3= 200,000 $250,000 + $125,000 + 25,000 = 400,000/3= 133,333.33
The best decision using the equal likely criterion the best choice is the investment of $266,666.666.
Decision Analysis
Questions 1-6 refer to the following
A family business is considering making an investment in its manufacturing operation. Three decisions are under consideration: (1) a large investment; (2) a medium investment; and (3) a small investment. The business believes that there are three possible future outcomes for its product: (1) increasing demand; (2) stable demand; and (3) decreasing demand. The following payoff table describes the decision situation.
|States of Nature |
|Decision |Increasing Demand |Stable Demand |Decreasing Demand |
|Large Investment |$1,000,000 |$400,000 |-$600,000 |
|Medium Investment |500,000 |300,000 |-200,000 |
|Small Investment |250,000 |125,000 |25,000 |
1. Identify the best decision using the maximax criterion.
Maximax $1,000,000 $500,000 $250,000
The best decision using the maximax criterion is the large investment of $1,000,000 because it has the most payoff.
2. Identify the best decision using the maximin criterion.
Min -600,000 -200,000 25,000
The best decision using the maximin criterion is the small investment of $25,000.
3. Identify the best decision using the equal likely criterion.
Average $1,000,000 + $400,000 + (-600,000) = 800,000/3= 266,666.666 $500,000 + $300,000 + (-200,000) = 600,000/3= 200,000 $250,000 + $125,000 + 25,000 = 400,000/3= 133,333.33
The best decision using the equal likely criterion the best choice is the investment of $266,666.666.