Collective decision-making dynamics in hypernetworks

Abstract: This work describes a collective decision-making dynamical process in a multiagent system under the assumption of cooperative higher-order interactions within the community, modeled as a hypernetwork. The nonlinear interconnected system is characterized by saturated nonlinearities that describe how agents transmit their opinion state to their neighbors in the hypernetwork, and by a bifurcation parameter representing the community's social effort. We show that the presence of higher-order interactions leads to the unfolding of a pitchfork bifurcation, introducing an interval for the social effort parameter in which the system exhibits bistability. With equilibrium points representing collective decisions, this implies that, depending on the initial conditions, the community will either remain in a deadlock state (with the origin as the equilibrium point) or reach a nontrivial decision. A numerical example is given to illustrate the results.