Dynamics of efficiency: A simple model

We propose a simple model that describes the dynamics of efficiencies of competing agents. Agents communicate leading to increase of efficiencies of underachievers, and an efficiency of each agent can increase or decrease irrespectively of other agents. When the rate of deleterious changes exceeds a certain threshold, the system falls into a stagnant phase. In the opposite situation, the average efficiency improves with asymptotically constant rate and the efficiency distribution has a finite width. The leading algebraic corrections to the asymptotic growth rate are also computed.