Optimal convergence in fame game with familiarity

A modified fame game is proposed by introducing familiarity between agents in the evolution process. We assume that since an agent is recommended, the forgotten probability by the taker decreases with the times that it has been recommended. At the same time, a tunable parameter is introduced to character the correlation between interaction strength and the familiarity. We find that there exists an optimal parameter value leading to the fastest convergence. We attribute this optimal phenomenon to the balance between the recommendation efficiency and the success rate of recommendation. Moreover, some other relevant characters, such as the time interval of forgetting each agent and the success rate of recommendation, are also investigated to understand the dynamics of the modified fame game.