Impacts of an expert’s opinion on the collective performance of a competing population for limited resources

The dissemination of information and opinion to the public has never been easier due to the easy access to platforms, making it necessary to study the responses to public information by a competing population. We study the impact of an expert’s opinion on the performance of a population including some die-hard fans of the expert and cautious agents who will adapt to trust or to ignore the expert’s opinion, within the framework of the minority game (MG). The expert collects information by probing a subpopulation for its minority opinion without the knowledge of its composition. When the information is not disseminated, the expert’s opinion has a higher accuracy than the intrinsic success rate of the population. When the information is disseminated, the population could enhance its success rate by making use of the wasted winning quotas through the actions of the fans and the adaptive ability of the cautious agents, as long as the fraction of the fans is not too big to turn the expert’s opinion into the losing option. There exists an optimal fraction of followers, the fans plus those cautious agents adapted to trust the expert, for the population to be the most harmonious with the highest success rate allowed by MG. The phenomena observed by numerical simulations motivated us to develop a theory, using the intrinsic success rate SrI, a quantity related to how the expert collects his information, and the average adapted level of trust f¯ among the cautious agents as inputs. The theory gives excellent agreement with simulation results, even when an approximated form of f¯ is invoked. The work paves the way for studying and formulating theories for the dissemination of other forms of information and opinion.