Game Theory and Best Decision

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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....
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