Consensus of Conspecific Agents via Collaborative and Antagonistic Interactions Available to Purchase

The vast majority of the existing agent-based models of consensus consider the interactions among the agents to be collaborative. In the present work, we define superimposed stochastically-switching network topologies which capture collaborative and antagonistic interactions among the agents. We consider a general class of agents, so-called conspecifics, which encompasses a wide range of protocols explored in the literature, ranging from Erdos-Renyi random networks to numerosity-constrained networks. We find closed form expressions for necessary and sufficient conditions for consensus. We validate the main results using Monte Carlo simulations and study the consensus conditions for Erdos-Renyi networks. We find that, for certain selections of system parameters, the presence of antagonistic interactions permits consensus in systems that would not reach accordance otherwise.