Problem of optimal strategy in the models of conflict redistribution of the resource space

Abstract

The theory of conflict dynamical systems is applied to finding of the optimal strategy in the problem of redistribution of the resource space between two opponents. In the case of infinite fractal division of the space, we deduce an explicit formula for finding the Lebesgue measure of the occupied territory in terms of probability distributions. In particular, this formula gives the optimal strategy for the occupation of the whole territory. The necessary and sufficient condition for the parity distribution of the territory are presented.