The Atkinson Inequality Index in Multiagent Resource Allocation

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 agreeing 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 in practice there are significant computational hurdles to be overcome: finding an optimal allocation is computationally intractable---independently of the approach chosen---and large numbers of potentially highly complex deals may be required under the distributed approach. From a methodological point of view, while much work in multiagent resource allocation relies on combinatorial arguments, here we use insights from basic calculus.