Reduction of economic inequality in combinatorial domains

Criteria for measuring economic inequality, such as the Lorenz curve and the Gini index, are widely used in the social sciences but have hardly been explored in Multiagent Systems, even though the significance of other concepts from fair division is widely accepted in the field. In a departure from the standard model used in Economics, we apply inequality criteria to allocation problems with indivisible goods, i.e., to the kind of problem typically analysed in Multiagent Systems. This gives rise to the combinatorial optimisation problem of computing an allocation that reduces inequality with respect to an initial allocation (and the closely related problem of minimising inequality), for a chosen inequality measure. We define this problem, we discuss the computational complexity of various aspects of it, and we formulate a generic approach to designing modular algorithms for solving it using integer programming.