Selfish Behavior and Resource Competition in Multi-Agent Systems

We study the convergence and equilibrium behavior of a large number of selfish agents who interact by queuing for sequentially acquired consumable resources. Examples of such systems include ridehailing and crowdsourcing platforms, systems with energy-like resources such as charging stations, and communication systems. Despite the generality of the agents' Markov decision process structures, this type of interaction permits a tractable characterization of equilibria. In particular, we leverage the property that these equilibria can be formulated as optimal solutions to an extended Eisenberg-Gale program, where time serves as an analog for money. Using this formulation, we (i) approximate equilibria via binary search, (ii) demonstrate Lyapunov stability for a broad class of learning dynamics, and (iii) establish global asymptotic stability of equilibria under replicator dynamics. Additionally, we prove Lyapunov stability for the coupled dynamics of queues and agents' replicator dynamics. When agents receive proportionally fair payoffs, they converge to an optimal set of actions, effectively behaving as if centrally coordinated.