Trajectories of Goods in Distributed Allocation
Yann Chevaleyre, Ulle Endriss, Nicolas Maudet

Abstract:
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.