Mechanistic origin of dragon-kings in a population of competing agents

We analyze the mechanistic origins of the extreme behaviors that arise in an idealized model of a population of competing agents, such as traders in a market. These extreme behaviors exhibit the defining characteristics of 'dragon-kings'. Our model comprises heterogeneous agents who repeatedly compete for some limited resource, making binary choices based on the strategies that they have in their possession. It generalizes the well-known Minority Game by allowing agents whose strategies have not made accurate recent predictions, to step out of the competition until their strategies improve. This generates a complex dynamical interplay between the number V of active agents (mimicking market volume) and the imbalance D between the decisions made (mimicking excess demand). The wide spectrum of extreme behaviors which emerge, helps to explain why no unique relationship has been identified between the price and volume during real market crashes and rallies.