Editing Centrality (section)

===Game-theoretic centrality===
The common feature of most of the aforementioned standard measures is that they assess the
importance of a node by focusing only on the role that a node plays by itself. However,
in many applications such an approach is inadequate because of synergies that may occur
if the functioning of nodes is considered in groups.

[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]

For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be a  good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.

Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last1=Hu |first1=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of eigenvector centrality. It is used to sort big data objects in Hu (2020),<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1| arxiv=2003.12198|doi-access=free}}</ref> such as ranking U.S. colleges.