Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game

Abstract

There is suggested a method of approximating unit-hypercubic infinite antagonistic game with the matrix game and the corresponding solution in finite strategies. The method is based on dimension-dependent irregular samplings over the game kernel. Numbers of the sampling points and their coordinates are chosen due to the stated conditions. If the sampled kernel is not the flat matrix them the multidimensional payoff matrix is reshaped into the flat one wherewith to solve the matrix game. The reshaping is a reversible matrix map. The concluding step of the approximation is in checking the finite solution consistency. Consistency can be weakened, and consistency can be checked at some rank corresponding to a natural number. The higher rank of the finite solution consistency is, the wider neighborhood of the sampling numbers at which the solution properties are monotonic-like.