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

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

Owen's coalitional value and aircraft landing fees

Air Transport;Game Theory

Non-centralized Control for Flow-based Distribution Networks: A Game-theoretical Insight

This paper solves a data-driven control problem for a flow-based distribution network with two objectives: a resource allocation and a fair distribution of costs. These objectives represent both cooperation and competition directions. It is proposed a solution that combines either a centralized or distributed cooperative game approach using the Shapley value to determine a proper partitioning of the system and a fair communication cost distribution. On the other hand, a decentralized noncooperative game approach computing the Nash equilibrium is used to achieve the control objective of the resource allocation under a non-complete information topology. Furthermore, an invariant-set property is presented and the closed-loop system stability is analyzed for the non cooperative game approach. Another contribution regarding the cooperative game approach is an alternative way to compute the Shapley value for the proposed specific characteristic function. Unlike the classical cooperative-games approach, which has a limited application due to the combinatorial explosion issues, the alternative method allows calculating the Shapley value in polynomial time and hence can be applied to large-scale problems.Generalitat de Catalunya FI 2014Ministerio de Ciencia y Educación DPI2016-76493-C3-3-RMinisterio de Ciencia y Educación DPI2008-05818Proyecto europeo FP7-ICT DYMASO

Socially Trusted Collaborative Edge Computing in Ultra Dense Networks

Small cell base stations (SBSs) endowed with cloud-like computing capabilities are considered as a key enabler of edge computing (EC), which provides ultra-low latency and location-awareness for a variety of emerging mobile applications and the Internet of Things. However, due to the limited computation resources of an individual SBS, providing computation services of high quality to its users faces significant challenges when it is overloaded with an excessive amount of computation workload. In this paper, we propose collaborative edge computing among SBSs by forming SBS coalitions to share computation resources with each other, thereby accommodating more computation workload in the edge system and reducing reliance on the remote cloud. A novel SBS coalition formation algorithm is developed based on the coalitional game theory to cope with various new challenges in small-cell-based edge systems, including the co-provisioning of radio access and computing services, cooperation incentives, and potential security risks. To address these challenges, the proposed method (1) allows collaboration at both the user-SBS association stage and the SBS peer offloading stage by exploiting the ultra dense deployment of SBSs, (2) develops a payment-based incentive mechanism that implements proportionally fair utility division to form stable SBS coalitions, and (3) builds a social trust network for managing security risks among SBSs due to collaboration. Systematic simulations in practical scenarios are carried out to evaluate the efficacy and performance of the proposed method, which shows that tremendous edge computing performance improvement can be achieved.Comment: arXiv admin note: text overlap with arXiv:1010.4501 by other author

Cases in Cooperation and Cutting the Cake

Cooperative game;sharing problem