Quantum Replicator Dynamics

Abstract

We propose quantization relationships which would let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. The quantum version of the replicator dynamics is the equation of evolution of mixed states from quantum statistical mechanics. A system and all its members will cooperate and rearrange its states to improve their present condition. They strive to reach the best possible state for each of them which is also the best possible state for the whole system. This led us to propose a quantum equilibrium in which a system is stable only if it maximizes the welfare of the collective above the welfare of the individual. If it is maximized the welfare of the individual above the welfare of the collective the system gets unstable and eventually it collapses.