Consensus Control Driven by Value Exchange

A multi-agent system is a system consisting of multiple agents that can make a global decision autonomously. So far, many studies have been conducted under the assumption that all agents behave cooperatively. On the other hand, in a large-scale multi-agent system such as a connected vehicle network, each agent must be owned by different owners. Thus, in such a system, the agents do not necessarily work cooperatively and each agent pursues its utility. Such a multi-agent system is modeled as a system driven by the exchange of certain values. In this paper, we address a consensus problem for a multi-agent system driven by the exchange between tokens and information. Unlike the typical consensus control, we assume that each agent has tokens and collects information from its neighbors in exchange for tokens. To this system, we derive a necessary and sufficient condition for the system to achieve consensus. This condition is characterized by the number of tokens and the network structure. Moreover, we disclose that the consensus value is given by the left eigenvector of the Perron matrix associated with the initial token distribution. Finally, we discuss the convergence property for several specific network structures.