  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.
