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.

Shapley Value: its algorithms and application to supply chains

“…Chao-hui [5], developed a new revenue allocation strategy based on the Shapley method principle, they took into account a risk coefficient, and an investment to improve the effects of the profits allocation, allowing the distribution of benefits reasonably and ensuring the persistence of the alliance and stability in the supply chain cooperation. This research was motivated by the fact that the original algorithm cannot fully mobilize the enthusiasm of partners, which prevent that cooperation in supply chain management being totally optimal.…”

“…Shapley Value is a way to attribute the economic output of a team to the individual members of that team [4]. It is probably the most important regulatory payoff scheme in coalition games [5].…”

A Study of Proxies for Shapley Allocations of Transport Costs

“…Allocation concepts are not solely devised and employed for allocating costs. For example, the Shapley value has been used to measure the importance of agents in social networks (Moretti & Patrone, 2008), and to measure the centrality of nodes in networks (Michalak, Aadithya, Szczepanski, Ravindran, & Jennings, 2013).…”

Parallelization of game theoretic centrality algorithms

“…This makes it suitable to be applied in the context of information diffusion. Polynomial time algorithms to compute game theoretic centrality were introduced by Tomasz Michalak et al (2013).…”

“…In section 3, we present the challenges in the parallelization using hadoop. In section 4, we present the five game-theoretic centrality algorithms proposed in Tomasz Michalak et al (2013) and the techniques to parallelize these algorithms in hadoop. In section 5, we evaluate the performance of our parallelized algorithms using the synthetic and real world data sets.…”