Question

. Describe, with examples, each of the various decision rules under uncertainty that we studied in class (e.g. maximin, leximin, etc). Why do some of these rules require utility to be cardinal? Which rule would you follow in making your own decisions and why?. Describe, with examples, each of the various decision rules under uncertainty that we studied in class (e.g. maximin, leximin, etc). Why do some of these rules require utility to be cardinal? Which rule would you follow in making your own decisions and why?

Answer 1

The maximin rule involves selecting the alternative that maximises the minimum pay-off achievable. The investor would look at the worst possible outcome at each supply level, then selects the highest one of these. The decision maker therefore chooses the outcome which is guaranteed to minimise his losses. In the process, he loses out on the opportunity of making big profits.

This approach would be appropriate for a pessimist who seeks to achieve the best results if the worst happens.

So, how many salads will Geoffrey decide to supply? Looking at the payoff table,

If we decide to supply 40 salads, the minimum pay-off is $80.
If we decide to supply 50 salads, the minimum pay-off is $0.
If we decide to supply 60 salads, the minimum pay-off is ($80).
If we decide to supply 70 salads, the minimum pay-off is ($160).
The highest minimum payoff arises from supplying 40 salads. This ensures that the worst possible scenario still results in a gain of at least $80.

The minimax regret strategy is the one that minimises the maximum regret. It is useful for a risk-neutral decision maker. Essentially, this is the technique for a 'sore loser' who does not wish to make the wrong decision.

'Regret' in this context is defined as the opportunity loss through having made the wrong decision.

To solve this a table showing the size of the regret needs to be constructed. This means we need to find the biggest pay-off for each demand row, then subtract all other numbers in this row from the largest number.

For example, if the demand is 40 salads, we will make a maximum profit of $80 if they all sell. If we had decided to supply 50 salads, we would achieve a nil profit. The difference or 'regret' between that nil profit and the maximum of $80 achievable for that row is $80.

Assigning of numerical values to the utility is normally known as cardinal utility. The theoretical quantity of utility is util. So models that incorporate with utility, use any other measurable quantity. For example one basket of orange give a consumer 10 utility while one basket of apple give the consumer 20 utility.

Please rate my answer.