Many of us do not like to get into a situation where there is very little information about external factors, or it is completely absent, and an important choice is urgently needed. Most likely, this is why most people prefer to avoid responsibility at work and are content with a modest, but at the same time relatively calm official position. If they knew about game theory and what benefits the criteria of Wald, Savage, Hurwitz could serve, the career of the most savvy of them would probably have gone up rapidly.
Count on the worst
This is how the first of these principles can be characterized. Wald's criterion is often called the criterion of extreme pessimism or the rule of minimal evil. In the conditions of limited resources and precarious, unstable situation, the reinsurance position, which is designed for the worst case, seems quite logical. Wald's maximin criterion focuses on maximizing gains in the most adverse circumstances. An example of its use is the maximum increase in the minimum income, the maximization of the minimum amount of cash, etc. This strategy justifies itself in cases where the decision maker is not so much interested in great luck as he wants to insure himself against sudden losses. In other words, Wald's criterion minimizes risk and allows you to make the most secure decisions. Such an approach makes it possible to obtain a guaranteed minimum, although the actual result may not be so bad.
Wald Criteria: Case Study
Suppose a certain company is going to produce new types of goods. In this case, a choice should be made between one of the four options B 1, B 2, B 3, B 4, each of which involves a certain type of release or a combination thereof. The decision will ultimately depend on which company will make a profit. How exactly the market will develop in the future is not known, however, analysts predict three main scenarios: С 1, С 2, С 3. The data obtained allow us to compile a table of possible winning options that correspond to each pair of a possible solution and a likely situation.
|
Types of products |
Market Scenarios |
Worst result |
||
|
C 1 |
C 2 |
C 3 |
||
|
In 1 |
25 |
37 |
45 |
25 |
|
In 2 |
50 |
22 |
35 |
22 |
|
In 3 |
41 |
90 |
fifteen |
fifteen |
|
At 4 |
80 |
32 |
20 |
20 |
Using the Wald criterion, you should choose the best strategy, one that will be most optimal for the enterprise in question. In our case, the performance indicator
E = max {25; 22; 15; 20} = 25.
We got it by choosing the minimum result for each of the options and isolating among them the one that will bring the greatest income. This means that the solution B 1 will be the most optimal for the company, according to this criterion. Even in the most adverse conditions, a result of 25 (C 1) will be obtained, at the same time it is possible that it will reach 45 (C 3).
We note again that Wald's criterion orientates a person to the most cautious line of behavior. In other circumstances, it is entirely possible to be guided by other considerations. For example, option B 3 could bring a gain of 90 with a guaranteed result of 15. However, this case is beyond the scope of the topic of this article, and therefore we will not consider it yet.
