1,479 research outputs found
Variance Allocation and Shapley Value
Motivated by the problem of utility allocation in a portfolio under a
Markowitz mean-variance choice paradigm, we propose an allocation criterion for
the variance of the sum of possibly dependent random variables. This
criterion, the Shapley value, requires to translate the problem into a
cooperative game. The Shapley value has nice properties, but, in general, is
computationally demanding. The main result of this paper shows that in our
particular case the Shapley value has a very simple form that can be easily
computed. The same criterion is used also to allocate the standard deviation of
the sum of random variables and a conjecture about the relation of the
values in the two games is formulated.Comment: 20page
Efficient computation of the Shapley value for game-theoretic network centrality
The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo
Allocation in Practice
How do we allocate scarcere sources? How do we fairly allocate costs? These
are two pressing challenges facing society today. I discuss two recent projects
at NICTA concerning resource and cost allocation. In the first, we have been
working with FoodBank Local, a social startup working in collaboration with
food bank charities around the world to optimise the logistics of collecting
and distributing donated food. Before we can distribute this food, we must
decide how to allocate it to different charities and food kitchens. This gives
rise to a fair division problem with several new dimensions, rarely considered
in the literature. In the second, we have been looking at cost allocation
within the distribution network of a large multinational company. This also has
several new dimensions rarely considered in the literature.Comment: To appear in Proc. of 37th edition of the German Conference on
Artificial Intelligence (KI 2014), Springer LNC
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
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