Resource Allocation with Population Dynamics

We study the problem of provisioning of information about the state of a system of shared resources to its users, assuming the state of the system is a result of the actions of the users and that the information about the state, in turn, drive the actions of the users. We extend the formulation of Marecek et al. [Int. J. Control 88( 10), 2015], such that the evolution of a heterogeneous population of users is governed by a Markov chain. Still, we are able to show that the distribution of users across the resources converges in distribution, for suitable means of provisioning the information about the system, under certain assumptions. The model and proof techniques may have wider applicability.