Stability of Leaderless Resource Consumption Networks

In this paper, we study the global stability properties of a multi-agent model of natural resource consumption, which balances ecological and social network components in determining the consumption behavior of a group of agents. Recently, it was shown that if the social network component of the model is leaderless, a condition that ensures that no single node has a greater social influence than any other node on the dynamics of the resource consumption, then the behavior of a group of agents can be treated in aggregate. This aggregation facilitates the application of this model to large scale networks, however it is as yet poorly understood. This paper shows that any network structure can be made leaderless by the social preferences of the agents. It is also shown that if the social network is leaderless, a mild bound on agents' environmental concern is sufficient for global asymptotic stability to a positive consumption value; indicating that appropriately configured networks can consume without depleting the resource. The behavior of these leaderless resource consumption networks is discussed via simulation.