Wealth concentration in systems with unbiased binary exchanges

Aiming to describe the wealth distribution evolution, several models consider an ensemble of interacting economic agents that exchange wealth in binary fashion. Intriguingly, models that consider an unbiased market, that gives to each agent the same chances to win in the game, are always out of equilibrium until the perfect inequality of the final state is attained. Here we present a rigorous analytical demonstration that any system driven by unbiased binary exchanges are doomed to drive the system to perfect inequality and zero mobility.