Codimension-2 Bifurcations in a Quantum Decision Making Model

Abstract

We consider a discrete-time model of a population of agents participating in a minority game using a quantum cognition in an approach with binary choices. As the agents make decisions based on both their present and past states, the model is inherently two-dimensional, but can be reduced to a one-dimensional system governed by a bi-valued function. Through this reduction, we prove how the complex bifurcation structure in the model’s 2D parameter space can be explained by a few codimension-2 bifurcation points of a type not yet reported in the literature. These points act as organizing centers for period-adding structures that partially overlap, leading to bistability.