Effect of imitation in a competing and evolving population in different situations

The effect of imitation in a competing and evolving population in different situations is studied. Agents in the population are repeatedly competing to be in a minority and they have a common strategy. Each agent has a parameter p characterizing the probability that he is following the prediction of the common strategy. Agents are lined up in a one-dimensional chain with periodic boundary condition. Imitation is allowed among nearest neighboring agents. Numerical results show that the phase transition appears, when the prize-to-fine ratio R is smaller than a given value, the strategy distribution of the population turns into a symmetric, inverted U shape. Consequently, imitation is harmful in a sense of enhancement in the overall performance of the population.