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.

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.

Several real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.

We present a new interpretation of the traditional computational social choice framework, where what are traditionally the candidates are construed as the agents. The particular implementation in mind is the proposed system for determining the medal winners for sports climbing in the 2020 Olympic games. We consider the issues of ties and of potential manipulation with respect to this interpretation. Simulation results suggest that for the proposed system ties are unlikely to be a problem, but that there is at least potential for manipulation, of a novel type. We formalise this conception of manipulation axiomatically. The strongest axioms lead to an impossibility along the lines of Arrow's impossibility, while a small weakening leads to a possibility. We also provide a hardness result concerning the determination of possible manipulation.

We introduce tool auctions, a novel market mechanism for constructing a cost-efficient assembly line for producing a desired set of products from a given set of goods and tools. Such tools can be used to transform one type of good into a different one. We then study the computational complexity of tool auctions in detail, using methods from both classical and parameterized complexity theory. While solving such auctions is intractable in general, just as for the related frameworks of combinatorial and mixed auctions, we are able to identify several special cases of practical interest where designing efficient algorithms is possible.

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.