Computing the Shapley value in allocation problems: approximations and bounds, with an application to the Italian VQR research assessment program

Abstract

In allocation problems with indivisible goods, money compensation is used to distribute worth in a fair way. Coalitional games provide a formal mathematical framework to model such problems, and the Shapley value is a solution concept widely used to realise a fair distribution. To overcome its intractability, we describe how to simplify allocation problems and we propose algorithms for computing lower bounds and upper bounds of the Shapley value that can be combined with approximation algorithms. The proposed techniques have been implemented and tested on a real-world application of allocation problems, namely, the Italian research assessment program known as VQR