Hierarchical games with restrictions on content and volume of information transfered

Two players hierarchical game is investigated. The top-level player is supposed to have right to first move. It is supposed that he has access to some information about his partner’s choice. But two types of restrictions on such information are taken into consideration. From one hand there are such pairs of bottom-level player choices that elements of pair are not distinguished one from another from the top level-player’s point of view. From other hand the volume of information on the bottom-level player’s choice which the top-level player can handle is restricted. The combinatorial approach (in terms of A.N. Kolmogorov) is used for measuring of the amount of information. Top level player is supposed to have the right of choice of the “sense” of information obtained (in the framework of restrictions of the first type). It is assumed that the top-level player knows the opportunity and goals of his partner and he can expect to rational behavior of his partner. In such assumptions the problem of calculating of the top level player’s maximal guaranteed result is a problem of calculating a maxima on complex functional spaces. In the article the problem is reduced to calculation of multiple maximin on “finite-dimensional” spaces. Two approaches to computing of this result are proposed. A structure of top level player’s optimal strategy is estimated. In particular the optimal semantics of information which top laver player handle is estimated. An illustrative example is provided which demonstrates the possibilities of use of methods proposed.