Complexity of finding Pareto-efficient allocations of highest welfare - Péter Biró; Jens Gudmundsson (Hungarian Academy of Sciences, Institute of Economics, Centre for Economic and Regional Studies, 2020)
We allocate objects to agents as exemplified primarily by school choice. Welfare judgments of the object-allocating agency are encoded as edge weights in the acceptability graph. The welfare of an allocation is the sum of its edge weights. We introduce the constrained welfare-maximizing solution, which is the allocation of highest welfare among the Pareto-efficient allocations. We identify conditions under which this solution is easily determined from a computational point of view. For the unrestricted case, we formulate an integer program and find this to be viable in practice as it quickly solves a real-world instance of kindergarten allocation and large-scale simulated instances. Incentives to report preferences truthfully are discussed briefly.
Keywords: C6; C78; D61; 330; Assignment; Pareto-efficiency; Welfare-maximization; Complexity; Integer programming