Consensus Protocols in Networks With 1-to-$n$ Joint-Agent Interactions

In the scientific literature of the past two decades many conditions to assess consensus-ability in multiagent networks with 1-to-1 interactions have been proposed. More recently the framework has been extended to include the $m$-to-1 type-interactions, referred as joint-agent interactions. In this article, we consider a novel framework of networks with 1-to-$n$ interactions, potentially extendable to $m$-to-$n$ ones, and formulate sufficient and necessary analytical conditions for consensus-ability. The considered interactions may also well represent the heterophilous dynamics in opinion and social systems. Finally, shedding light on the scenario of 1-to-$n$ interactions could inspire the formulation of new distributed algorithms to be exploited in engineering applications.