Minimising inequality in multiagent resource allocation Structural analysis of a distributed approach

We analyse the problem of finding an allocation of resources in a multiagent system that is as fair as possible in terms of minimising inequality between the utility levels enjoyed by the individual agents. We use the well-known Atkinson index to measure inequality and we focus on the distributed approach to multiagent resource allocation, where new allocations emerge as the result of a sequence of local deals between groups of agents who agree on an exchange of some of the items in their possession. Our results show that it is possible to design systems that provide theoretical guarantees for optimal outcomes that minimise inequality, but also that there are significant computational hurdles to be overcome in the worst case. In particular, finding an optimal allocation is computationally intractable and under the distributed approach a large number of structurally complex deals, possibly involving many agents and items, may be required before convergence to a socially optimal allocation. This remains true even in severely restricted resource allocation scenarios where all agents have the same utility function. From a methodological point of view, while much work in multiagent resource allocation relies on combinatorial arguments, here we instead use insights from basic calculus.