Towards a fair VQR with the aid of database (and game) theory

In a great number of applications, it is necessary to distribute resources or tasks to agents collaborating with each other in a network in order to maximize the overall social welfare. The question in these cases is how to divide in a fair way the outcome that the network eventually earns, say money, to the participating agents. The paper faces this issue by focusing on a real-world application: the distribution of funds to Italian research structures and substructures, after a research assessment program (known as VQR) that is currently evaluating the Italian research production over years 2011-2014. In fact, we report our recent results in [1], for allocation problems that find application to the VQR. In particular, we describe a number of desirable properties for any reasonable fair division rule, we identify a division rule satisfying all such properties, as well as algorithms for its computation. The proposed solution is based on the gametheoretic notion of Shapley value, and the algorithms for its computation exploit recent advances in the problem of counting solutions to conjunctive queries.