We propose a dynamical model of a competing population whose agents have a tendency to balance their decisions in time. The model is applicable to financial markets in which the agents trade with finite capital or to other multiagent systems, such as routers in communication networks attempting to transmit multiclass traffic in a fair way. We find an oscillatory behavior of the model which is explainable by the segregation of agents into two groups. Each group remains winning over epochs. The aggregation of smart agents is able to explain the lifetime distribution of epochs to 8 decades of probability.