Inequality measures in kinetic exchange models of wealth distributions

•Inequality in kinetic exchange models of wealth distributions.•Lower and upper bounds of inequality indices.•Phase diagram of Gini index and kk-index.•Analytical formulas for gamma and double gamma distributions to calculate inequalities.

In this paper, we study the inequality indices for some models of wealth exchange. We calculated Gini index and newly introduced kk-index and compare the results with reported empirical data available for different countries. We have found lower and upper bounds for the indices and discuss the efficiencies of the models. Some exact analytical calculations are given for a few cases. We also exactly compute the quantities for Gamma and double Gamma distributions.