On the emergence of oscillations in distributed resource allocation

We consider the problem of resource allocation in a decentralized 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 characterize in this case the limiting behaviours of trajectories. Methods of modifying the dynamics are also given, such that convergence to an optimal solution is guaranteed.