  The inequality in capital or resource distribution is among the important
phenomena observed in populations. The sources of inequality and methods for
controlling it are of practical interest. To study this phenomenon, we
introduce a model of interaction between agents in the network designed for
reducing the inequality in the distribution of capital. To achieve the effect
of inequality reduction, we interpret the outcome of the elementary game played
in the network such that the wining of the game is translated into the
reduction of the inequality. We study different interpretations of the
introduced scheme and their impact on the behaviour of agents in the terms of
the capital distribution, and we provide examples based on the capital
dependent Parrondo's paradox. The results presented in this study provide
insight into the mechanics of the inequality formation in the society.
