Pricing Mechanism for Resource Sustainability in Competitive Online Learning Multi-Agent Systems

In this paper, we consider the problem of resource congestion control for competing online learning agents. On the basis of non-cooperative game as the model for the interaction between the agents, and the noisy online mirror ascent as the model for rational behavior of the agents, we propose a novel pricing mechanism which gives the agents incentives for sustainable use of the resources. Our mechanism is distributed and resource-centric, in the sense that it is done by the resources themselves and not by a centralized instance, and that it is based rather on the congestion state of the resources than the preferences of the agents. In case that the noise is persistent, and for several choices of the intrinsic parameter of the agents, such as their learning rate, and of the mechanism parameters, such as the learning rate of -, the progressivity of the price-setters, and the extrinsic price sensitivity of the agents, we show that the accumulative violation of the resource constraints of the resulted iterates is sub-linear w.r.t. the time horizon. Moreover, we provide numerical simulations to support our theoretical findings.