On the emergence of oscillations in distributed resource allocation

We consider the problem of resource allocation in a decentralised market where users and suppliers trade for a single commodity. Due to the lack of strict concavity, convergence to the optimal solution by means of classical gradient type dynamics for the prices and demands, is not guaranteed. In the paper we explicitly characterise in this case the asymptotic behaviour of trajectories and provide an exact characterisation of the limiting oscillatory solutions. Methods of modifying the dynamics are also given, such that convergence to an optimal solution is guaranteed, without requiring additional information exchange among the users.