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Hierarchical games with restrictions on the amount of information transmitted

The paper examines a new class of models, the common feature of which is the presence of a limited volume of information exchanges between players. It is shown that taking such restrictions into account allows one to significantly expand the class of situations that can be adequately described using the games in normal form. Possible ways of formalizing the concept of “amount of information” are discussed, returning to the constructions by A.N. Kolmogorov. A new concept of the maximal guaranteed result is discussed. The application of the outlined ideas in the information theory of hierarchical systems is considered.