  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.
