Decision Theory: Analyzing Payoff Tables and Decision Strategies

This assignment delves into decision-making strategies using payoff tables, covering optimistic, conservative, and minimax regret approaches. It analyzes profit and cost payoff tables to determine optimal decisions under different states of nature. The assignment also includes graphical sensitivity analysis to assess the impact of changing probabilities on decision outcomes. Several questions explore practical applications of decision theory, such as service pricing strategies and investment decisions, incorporating expected value calculations and risk assessment. The analysis extends to evaluating the value of perfect information and the impact of promotional campaigns on decision-making processes. The assignment showcases how different decision-making approaches can lead to varying recommendations based on risk tolerance and available information.

MATHS ASSIGNMENT 8
Student NAME:
[Pick the date]

Question 2
Profit payoff table for the four states of nature along with the decision strategy is shown below.
(a) Optimistic approach to get the maxi-max for the payoff matrix is shown below.
Decision 1 (D1) with respect to the MAXIMAX payoff is the preferred decision.
 Conservative approach to get the maximum for the payoff matrix of the decisions is shown
below.
Decision 3 (D3) with respect to the MAXIMIN payoff is the preferred decision.
1

 Minimum regret approach to get the minimum for the payoff matrix of losses of the decision is
shown below.
Decision 2 and 3 (D1 and D3) with respect to the MINIMAX payoff form the requisite decision.
(b) MINIMAX decision procedure
Decision 1 (D1) with respect to the MINIMAX cost is the needed decision.
(c) Optimistic approach to get the MINIMUM for the cost matrix of the decisions is shown
below.
Decision 1 (D1) with respect to the MINIMAX cost is the needed decision.
 Conservative approach to get the MINIMAX for the payoff matrix of the decisions is shown
below.
2

Decision 2 and 3 (D2 and D3) with respect to the MAXIMAX cost is the needed decision.
Question 8
Payoff matrix
(a) Graphical sensitivity analysis
3

Here,
(b)
(c) It is apparent that the best decision would be with
This would be continue optimal decision until the expected value is more than for
Let’s
It can be said that the best decision would be until payoff for s under state nature 1 >= 2.
4

Question 9
(a) The decision would be made for the various types of services which are provided. The
probability event would be the strength of the demand that would be occurred. Quarterly
profit or quarterly loss would be an imperative aspect to consider. “Strong demand and weak
demand are the two expected outcomes for chance events.”
(b) Optimistic approach: Demand would be assumed to be strong demand. It means full price
would be charged which then would result in high profit.
Conservative approach: Demand would be assumed to be weak demand. It means discounted
price would be given which would then result in high profit.
Minimax regret approach: Demand would be strong demand when the firm is charging full price
and maximum profit has achieved. Thereby, no regret would be present. Further, demand would
be weak demand when the firm is charging full price and loss of value $490 has received.
However, the firm could make a profit of $320 by decreasing the prices. Therefore, the firm
would have a regret of ($320-(-$490) = $810. In case of full price is charged then the maximum
regret would be $810.
Further, if discount has been offered and demand becomes weak, then the firm would maximize
the profit and no regret would occur. However, if discount has been offered and demand
becomes strong, then the firm would make the profit of $670 whereby, the firm can make a profit
of $960. Hence, the firm would have a regret of ($960-(-$670) =$290. In case of full price being
charged , then the maximum regret would be $290.
Hence, Firm should provide the discount in order to minimize the total regret.
(c)
Expected value is higher in case of providing discount and hence, discount should be chosen.
5

(d)
Expected value is higher in case of full price service and hence, full price service should be
chosen.
(e) Let probability of strong demand is p.
Discount service should be selected when the p is lower than 0.736. Similarly, full price service
should be selected when the p is higher than 0.736.
Question 14
Payoff table
6

(a) Optimal decision strategy when perfect information is available
State of nature s1
Decision strategy d1
Profit =250
Similarly,
State of nature s2
Decision strategy d1 or d2
Profit =100 (same profit)
Further,
State of nature s3
Decision strategy d2
Profit =75
(b) Expected value for decision strategy
(c) Expected value for decision strategy when perfect information is not available
Expected value for decision strategy 1
Expected value for decision strategy 2
7

Expected value for decision strategy 1 is higher than strategy 2, when the perfect information is
not available. Therefore, the right expected value would be 182.5.
(d) Expected value for perfect information
Question 15
Net cash flow
(a) Expected value approach
Large or medium any type of sized centers can be taken into account as they show same
expected value.
(b) Risk profits for median and large alternatives
8

Risk of medium center =
Risk of large center =
It can be seen that large center has high risk and hence, medium center would be recommended.
(c)Expected value for perfect information
Additional information would be beneficial for the city because it increases the net cash flow to
$122,000.
(d)Change in the decision recommendation
9

Expected value is higher for small center and hence, it should be selected.
(e) Expenditure on promotional campaign= $150,000
Campaign has reduced the probability in case of worst scenario =0.00
Campaign has increased the probability in case of best scenario =0.4
It can be seen that expected value is higher for large center and hence, it should be selected.
10

11