Decision making under uncertainty is not only characterized by ignorance of the final outcome, as with risk, but also by the impossibility of assigning a probability of the outcome’s distribution, as this is also unknown. Both subjective and objective information is unavailable. However, there are a few different criteria that can be applied in order to choose one strategy over others, when facing a decision under uncertainty.
Considering three potential nature states (N1, N2, N3) and three possible strategies (S1, S2, S3) to follow. Their combination results in different outcomes. Let’s see how these criteria work using the example in the following figure:
1) Wald’s maximin model, also known as pessimist model: select the maximum of the minimum, in other words the lesser of evils. We choose S1, since -3>-5>-7;
2) Optimist model (maximax): select the maximum of the maximum, the best amongst the best. We choose S2 since 9>6>2;
3) Laplace criterion: equal probabilities are assigned to the result of each strategy, from which the highest is chosen. We choose S3 because 10/3>5/3>0 (S3>S2>S1);
4) Hurwicz criterion or optimist-pessimist index: an optimum constant (α) is defined and assigned to the best result, and another is assigned to the worst (1-α). The average weighted value is then calculated and the highest value is chosen. The results will depend on the value of the constant (α) defined.
5) Savage criteria or “minimax Regret”: the agent determines the maximum results for the competitor and choses the strategy that will lead his competitor to the lowest result. This will make the agent better-off.