Stability of Leaderless Resource Consumption Networks

Abstract

In this paper, we study the global stability properties of a multi-agent model of natural resource consumption that balances ecological and social network components in determining the consumption behavior of a group of agents. The social network is assumed to be leaderless, a condition that ensures that no single node has a greater influence than any other node on the dynamics of the resource consumption. It is shown that any network structure can be made leaderless by the social preferences of the agents. The ecological network component includes a quantification of each agent's environmental concern, which captures each individual agent's threshold for when a resource becomes scarce. We show that leaderlessness and a mild bound on agents' environmental concern are jointly sufficient for global asymptotic stability of the consumption network to a positive consumption value, indicating that appropriately configured networks can continuously consume a resource without driving its value to zero. The behavior of these leaderless resource consumption networks is verified in simulation.