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

In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximized, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money compensation to perform a fair allocation taking into account the actual contribution of all agents to the social welfare. Coalitional games provide a formal mathematical framework to model such problems, in particular the Shapley value is a solution concept widely used for assigning worths to agents in a fair way. Unfortunately, computing this value is a #P-hard problem, so that applying this good theoretical notion is often quite difficult in real-world problems. In this paper, we first review the application of the Shapley value to an allocation problem that models the evaluation of the Italian research structures with a procedure known as VQR. For large universities, the problem involves thousands of agents and goods (here, researchers and their research products). We then describe some useful properties that allow us to greatly simplify many such large instances. Moreover, we propose new algorithms for computing lower bounds and upper bounds of the Shapley value, which in some cases provide the exact result and that can be combined with approximation algorithms. The proposed techniques have been tested on large real-world instances of the VQR research evaluation problem

On the Shapley value and its application to the Italian VQR research assessment exercise

Research assessment exercises have now become common evaluation tools in a number of countries. These exercises have the goal of guiding merit-based public funds allocation, stimulating improvement of research productivity through competition and assessing the impact of adopted research support policies. One case in point is Italy's most recent research assessment effort, VQR 2011–2014 (Research Quality Evaluation), which, in addition to research institutions, also evaluated university departments, and individuals in some cases (i.e., recently hired research staff and members of PhD committees). However, the way an institution's score was divided, according to VQR rules, between its constituent departments or its staff members does not enjoy many desirable properties well known from coalitional game theory (e.g., budget balance, fairness, marginality). We propose, instead, an alternative score division rule that is based on the notion of Shapley value, a well known solution concept in coalitional game theory, which enjoys the desirable properties mentioned above. For a significant test case (namely, Sapienza University of Rome, the largest university in Italy), we present a detailed comparison of the scores obtained, for substructures and individuals, by applying the official VQR rules, with those resulting from Shapley value computations. We show that there are significant differences in the resulting scores, making room for improvements in the allocation rules used in research assessment exercises

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

In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money compensation to perform a fair allocation taking into account the actual contribution of all agents to the social welfare. Coalitional games provide a formal mathematical framework to model such problems, in particular the Shapley value is a solution concept widely used for assigning worths to agents in a fair way. Unfortunately, computing this value is a #P-hard problem, so that applying this good theoretical notion is often quite difficult in real-world problems. We describe useful properties that allow us to greatly simplify the instances of allocation problems, without affecting the Shapley value of any player. Moreover, we propose algorithms for computing lower bounds and upper bounds of the Shapley value, which in some cases provide the exact result and 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 (Verifica della Qualità della Ricerca, or Research Quality Assessment)1. For the large university considered in the experiments, the problem involves thousands of agents and goods (here, researchers and their research products). The algorithms described in the paper are able to compute the Shapley value for most of those agents, and to get a good approximation of the Shapley value for all of the

Energy optimization through traffic aggregation in wireless networks

Abstract—Cellular networks can provide pervasive data ac-cess for smartphones, but also consume lots of energy, because the cellular interface has to stay in high power state for a long time (called long tail problem) after a data transmission. In this paper, we propose to reduce the tail energy by aggregating the data traffic of multiple nodes using their P2P interfaces. This traffic aggregation problem is formalized as finding the best task schedule to minimize energy. We first propose an A search algorithm, which can reduce the search space for finding the optimal schedule offline, and then introduce an online traffic aggregation algorithm. We have implemented the online traffic aggregation algorithm on Android smartphones, and have built a small testbed. Trace-driven simulations and Experimental results show that our traffic aggregation algorithm can significantly reduce the energy and delay. I