Evolutionary Minority Game with Multiple Options

We propose and study an evolutionary minority game (EMG) in which the agents are allowed to choose among three possible options. Unlike the original EMG where the agents either win or lose one unit of wealth, the present model assigns one unit of wealth to the winners in the least popular option, deducts one unit from the losers in the most popular option, and awards $R$ ($-1<R< 1$) units for those in the third option. Decisions are made based on the information in the most recent outcomes and on the characteristic probabilities of an agent to follow the predictions based on recent outcomes. Depending on $R$, the population shows a transition from self-segregation in difficult situations ($R<R_{c}$) in which the agents tend to follow extreme action to cautious or less decisive action for $R>R_{c}$, where $R_{c}(N)$ is a critical value for optimal performance of the system that drops to zero as the number of agents $N$ increases.