/ / Wald Criterion, or How to get the best guaranteed result

Wald Criterion, or How to get the best guaranteed result

Many of us do not like to get into a situation whereinformation on external factors is very small, 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 quiet official position. If they knew about the theory of games and how the criteria of Wald, Savage, Hurwitz could serve, the career of the most intelligent of them would surely have swiftly gone up.

vald criterion

Count on the worst

This is how you can characterize the first oflisted principles. The Wald criterion is often called the criterion of extreme pessimism or the rule of minimal evil. In conditions of limited resources and a shaky, unstable position, it seems logical to assume a reinsurance position, which is designed for the worst case. Maxim's Wald criterion focuses on maximizing winnings in the most unfavorable circumstances. An example of its use can serve as a maximum increase in the minimum income, maximize the minimum amount of cash, etc. Such a strategy justifies itself in those cases when the decision-maker is not so much interested in big luck as he wants to hedge against sudden losses. In other words, Wald's criterion reduces the risk to a minimum and allows making the most secure decisions. Such an approach makes it possible to obtain a guaranteed minimum, although the actual result may not be so bad.

criteria for Valdha Savage Hurwitz

Wald criterion: an example of use

Suppose an enterprise is going to produce new types of goods. In this case, one should choose between one of the four variants B1, AT2, AT3, AT4, each of which assumes a certain typeissue or a combination thereof. From the decision-making will ultimately depend on which enterprise will make a profit. How the market situation will develop in the future is unknown, but analysts predict three main scenarios for the development of events: C1, FROM2, FROM3. The obtained data allow making a table of possible winning options that correspond to each pair of possible solutions and probable situation.

Types of products

Scenarios of market conditions

Worst result
























Using Wald's criterion, one should choose the best strategy, the one that will be most optimal for the company under consideration. In our case, the efficiency index

E = max {25; 22; 15; 20} = 25.

We got it by selecting the minimal result for each of the options and isolating among them the one that will bring the greatest revenue. This means that the solution B1 will be for the firm, according to this criterion, the most optimal. Even under the most unfavorable conditions, a result of 25 (C1), at the same time it is possible that it will reach 45 (C3).

maximally vald
We note once again that the Wald criterion is orientedman to the most cautious line of conduct. In other circumstances, it is entirely possible to be guided by other considerations. For example, option B3 could bring a gain of 90 with a guaranteed result of 15. However, this case is beyond the scope of this article, and therefore we will not consider it yet.

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