Hybrid consensus for averager–copier–voter networks with non-rational agents

For many social dynamical systems with heterogenous communicating components there exist non-rational agents, whose full profile (such as location and number) is not accessible to the normal agents a priori, posing threats to the group goal of the community. Here we demonstrate how to provide resilience against such non-cooperative behaviors in opinion dynamics. We focus in particular on the consensus of a hybrid network consisting of continuous-valued averager, copier agents and discrete-valued voter agents, where the averagers average the opinions of their neighbors and their own deterministically, while copiers and voters update their opinions following some stochastic strategies. Based upon a filtering strategy which removes some fixed number of opinion values, we establish varied necessary and sufficient conditions for the hybrid opinion network to reach consensus in mean in the presence of globally and locally bounded non-rational agents. The communication topologies are modeled as directed fixed as well as time-dependent robust networks. Although our results are shown to be irrespective of the proportion of the averager, copier, and voters, we find that the existence of voters has distinct influence on the evolution and consensus value of the negotiation process.