Facilitating Matches on Allocation Platforms

We consider a setting where goods are allocated to agents by way of an allocation platform (e.g., a matching platform). An "allocation facilitator" aims to increase the overall utility/social-good of the allocation by encouraging (some of the) agents to relax (some of) their restrictions. At the same time, the advice must not hurt agents who would otherwise be better off. Additionally, the facilitator may be constrained by a "bound" (a.k.a. 'budget'), limiting the number and/or type of restrictions it may seek to relax. We consider the facilitator's optimization problem of choosing an optimal set of restrictions to request to relax under the aforementioned constraints. Our contributions are three-fold: (i) We provide a formal definition of the problem, including the participation guarantees to which the facilitator should adhere. We define a hierarchy of participation guarantees and also consider several social-good functions.