Effects of Contrarians in the Minority Game

We study the effects of the presence of contrarians in an agent-based model of competing populations. Contrarians are common in societies. These contrarians are agents who deliberately prefer to hold an opinion that is contrary to the prevailing idea of the commons or normal agents. Contrarians are introduced within the context of the Minority Game (MG), which is a binary model for an evolving and adaptive population of agents competing for a limited resource. Results of numerical simulations reveal that the average success rate among the agents depends non-monotonically on the fraction $a_{c}$ of contrarians. For small $a_{c}$, the contrarians systematically outperform the normal agents by avoiding the crowd effect and enhance the overall success rate. For high $a_{c}$, the anti-persistent nature of the MG is disturbed and the few normal agents outperform the contrarians. Qualitative discussion and analytic results for the small $a_{c}$ and high $a_{c}$ regimes are also presented, and the crossover behavior between the two regimes is discussed.