Decision theory, like VBSE theory, is a mathematical discipline that studies the decisions of an agent, most often an individual, whom she considers rational and considers in isolation from others.

Along with the theory of games and the theory of collective choice, this is one of the mathematical specialties of rational choice, which serves as a technical auxiliary tool for the economy and, much less often, for other social sciences. When, for example, sociology or political science pretend to theories of rational choice, they most often represent informal and strictly qualitative concepts, whose proximity to common sense is revealed spontaneously. Here we will not deal with this corpus, although it considers the same objects as in the three previous theories.

The group they form is structured, but not completely unified, and it differs differently depending on the preferred criterion and the choice of adaptive control type. Considering first the number and interaction of agents, we say that the solution theory is connected with the actions of an isolated individual, the theory of games with the actions of many and interacting individuals, and the theory of the collective choice of the actions of several people, but not interacting. The classification clearly separates the first theory from the other two, but formulated in this way threatens to turn it into a useless “robinsonade”, and since it actually claims to be used in real situations when agents are not isolated, you need to look for the best identification criterion. The one we are going to research, agent knowledge and its use, answers the question, approaching the subject of the article. When this is not clear, agent knowledge can be represented in two completely different ways.

Natural uncertainty refers to the dependency theory, when the agent ignores or imperfectly recognizes, but which, based on the needs of the decision that he must make, can be determined outside of him.

The hypothesis is suitable when these phenomena arise from an external nature; then they themselves are not the result of a decision and, in particular, they do not reflect the malicious intent of the alleged adversary. Strategic uncertainty is associated with decision theory, when an agent, on the contrary, must make, depending on his own decision, if he wants to make it correctly. This takes place in certain board games and in military strategy, at least when the latter is well understood, which is far from always the case. Then the agent believes that a phenomenon in which he is not sure is the result of decisions of other agents, made in his own way, albeit with different goals, which leads him into a dizzying sequence of mutual expectations. Game theory deals primarily with strategic uncertainty, responding with its concepts of balance to a complex problem arising from mutual expectation. As for decision theory, it deals exclusively with natural uncertainty, responding with its concepts of optimality to the simpler, but by no means trivial, problem of describing the best decision that an agent must make. the light of his anticipation, the only one then involved.

The strength of the previous difference is that it does not depend mainly on the nature of the phenomena to which expectation relates. Of course, a meteorologist who is interested in summer heat is not in the same mental situation as an election candidate who evaluates his chances in accordance with the chances of his competitors. But a meteorologist can act as a strategist if he believes that the heat waves are partially caused by the anthropogenic effect and that the more or less disturbing forecast he makes for them is likely to destroy this effect. And a politician may associate his chances of success less with the actions of competitors than at the end of a financial crisis, the price of which he does not affect and which he can then present as a natural phenomenon.

Thus, control theory is associated not so much with phenomena as with the agent itself and the rationality to which it corresponds; more precisely, the business of a theoretician who decides to represent the agent in accordance with one rational or another ideal type, taking into account the phenomenon under consideration. A roundness in which a clear distinction between the types of uncertainty and rationality strengthens the privilege of theoretical choice over empirical classification. Decision theory and game theory are ultimately characterized by their own view of situations that can be the same or very similar, the choice between them depends on idealizations that the observer considers preferable.