Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality

Abstract

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. For instance, in the case of unweighted networks our algorithms are able to return the exact solution about 1600 times faster than the Monte Carlo approximation, even if we allow for a generous 10% error margin for the latter method.

Cited by in corpus (10)

• Group based Centrality for Immunization of Complex Networks
• Conditional Dichotomy of Boolean Ordered Promise CSPs
• Towards a more efficient computation of individual attribute and policy contribution for post-hoc explanation of cooperative multi-agent systems using Myerson values
• Centralities in complex networks
• The Ranking Problem of Alternatives as a Cooperative Game
• Random partitions, potential, value, and externalities
• Modeling Spread of Preferences in Social Networks for Sampling-based Preference Aggregation
• Computing Vertex Centrality Measures in Massive Real Networks with a Neural Learning Model
• Efficient Shapley Performance Attribution for Least-Squares Regression
• FW-Shapley: Real-time Estimation of Weighted Shapley Values