Trajectories of goods in distributed allocation

Distributed allocation mechanisms rely on the agents' autonomous (and supposedly rational) behaviour: states evolve as a result of agents contracting deals and exchanging resources. It is no surprise that restrictions on potential deals also restrict the reachability of some desirable states, for instance states where goods are efficiently allocated. In particular topological restrictions make any attempt to guarantee asymptotic convergence to an optimal allocation impossible in most cases. In this paper, we concentrate on the dynamics of such systems; more precisely we study the trajectories of goods in such iterative reallocative processes. Our first contribution is to propose an upper bound on the length of the trajectories of goods, when agent utility functions are modular. The second innovative aspect of the paper is then to discuss how this affects, on average, the quality of the states that are reached. Finally, a preliminary study of the non-modular case is proposed, examining how synergetic effects between items can affect their trajectories.