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Constructing games on networks for controlling the inequalities in the capital distribution

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.