Question

1. Give an example of another scenario that you could create a payoff table for, what are the decision alternatives, states of nature, and payoffs?
2. Why do you think these methods are called “under ignorance”?

Answer 1

Answer: A profit table (pay­off table) can be a useful way to represent and analyze a scenario where there is a range of possible outcomes and a variety of possible responses. It simply illustrates all possible profits/losses and as such is often used in decision making under uncertainty.

For Example:

Bakim Das runs a Bakery that provides cupcakes for canteens throughout a large organization. A particular cupcake is sold to the canteen for $10 and costs $8 to prepare. Therefore, the contribution per salad is $2.

Based on past demands, it is expected that, during the 250 ­day working years, the canteens will require the following daily quantities:

• On 25 days of the year, 40 cupcakes.

• On 50 days of the year, 50 cupcakes.

• On 100 days of the year, 60 cupcakes.

• On 75 days 70 cupcakes.

The Bakery must prepare the cupcakes in batches of 10 meals in advance. The manager has asked you to help decide how many cupcakes the bakery should supply for each day of the forthcoming year.

Constructing a pay­off table:

If 40 cupcakes will be required on 25 days of a 250 day year, then the probability that demand = 40 cupcakes is

P(Demand of 40) = 25 days ÷ 250 days = 0.1

Likewise,

• P(Demand of 50) = 0 .20;
• P(Demand of 60) = 0.4 and
• P(Demand of 70) = 0.30

Now let's look at the different values of profit or losses depending on how many salads are supplied and sold.

For example, if we supply 40 cupcakes and all are sold, our profits amount to 40 x $2 = 80.

If however we supply 50 salads but only 40 are sold, our profits will amount to 40 × $2 -­ (10 unsold salads × $8 unit cost) = 80 - 80 = 0.

Similarly, we can now construct a pay­off table as follows:

Daily supply
Daily Demand		Probability	40 cupcakes	50 cupcakes	60 cupcakes	70 cupcakes
40 salads	0.10	$80	$0	$(80)	$(160)
50 salads	0.20	$80	$100	$20	$(60)
60 salads	0.40	$80	$100	$120	$40
70 salads	0.30	$80	$100	$120	$140

Decision Rules: Using the Min-Max method

To decide how many cupcakes should be made every day, Bakim will first have to define his attitude to risk, and use one of the following rules to make up his mind:

• The maximax rule for an optimist - i.e. someone who wants the best possible upside potential without being very concerned about possible losses or downside.
• The maximin rule for a pessimist looking to minimize his losses - i.e. someone who wants to minimize the potential downside exposure.
• The minimax regret rule is for someone who doesn't like making the wrong decision. This approach seeks to minimize such "regret".
• Alternatively, expected values of profits could be used to make a decision. These are averages and essentially ignore the spread or risk of outcomes. Risk must thus be brought back into the decision making process another

It is called 'Under Ignorance' because the decision maker(Here Bakim) has no information distinguishing the prospects of occurrences of the event ( here number cupcakes sold). Here he has no probabilities or any other measure over the space X. A number of different approaches can be used. What must always be kept in mind is the choice of any approach to be used is a subjective one, in deciding upon a method to compare the alternatives the decision-maker is implicitly using some personal preferences.