Axiomatic Characterization of Game-Theoretic Centrality

One of the fundamental research challenges in network science is centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this article, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been recently proposed based on this approach, it is still unknown how general is the game-theoretic approach to centrality and what distinguishes some game-theoretic centralities from others. In this article, we attempt to answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every possible centrality measure can be obtained following the game-theoretic approach. Furthermore, we study three natural classes of game-theoretic centrality, and prove that they can be characterized by certain intuitive properties pertaining to the well-known notion of Fairness due to Myerson.

[1]  Martin G. Everett,et al.  A Graph-theoretic perspective on centrality , 2006, Soc. Networks.

[2]  R. Myerson.  Conference structures and fair allocation rules , 1978 .

[3]  Michael Wooldridge,et al.  Hedonic coalition nets , 2009, AAMAS.

[4]  Ulrik Brandes,et al.  Network Analysis: Methodological Foundations , 2010 .

[5]  Sebastiano Vigna,et al.  Axioms for Centrality , 2013, Internet Math..

[6]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

[7]  Oskar Skibski,et al.  Defeating Terrorist Networks with Game Theory , 2015, IEEE Intelligent Systems.

[8]  Y. Narahari,et al.  Determining the top-k nodes in social networks using the Shapley value , 2008, AAMAS.

[9]  Stefan Richter,et al.  Centrality Indices , 2004, Network Analysis.

[10]  Oskar Skibski,et al.  Axiomatic Characterization of Game-Theoretic Network Centralities , 2017, AAAI.

[11]  Guillermo Owen,et al.  Centrality and power in social networks: a game theoretic approach , 2003, Math. Soc. Sci..

[12]  Makoto Yokoo,et al.  Attachment Centrality: An Axiomatic Approach to Connectivity in Networks , 2016, AAMAS.

[13]  J. Nieminen.  On the centrality in a graph. , 1974, Scandinavian journal of psychology.

[14]  Rafael Amer,et al.  A connectivity game for graphs , 2004, Math. Methods Oper. Res..

[15]  L. Freeman,et al.  Centrality in valued graphs: A measure of betweenness based on network flow , 1991 .

[16]  Oskar Skibski,et al.  Attachment Centrality for Weighted Graphs , 2017, IJCAI.

[17]  Yoav Shoham,et al.  Marginal contribution nets: a compact representation scheme for coalitional games , 2005, EC '05.

[18]  Y. Narahari,et al.  A Shapley Value-Based Approach to Discover Influential Nodes in Social Networks , 2011, IEEE Transactions on Automation Science and Engineering.

[19]  Oskar Skibski,et al.  A Shapley Value-based Approach to Determine Gatekeepers in Social Networks with Applications , 2014, ECAI.

[20]  Michael Wooldridge,et al.  Computational Aspects of Cooperative Game Theory , 2011, KES-AMSTA.

[21]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[22]  Herbert Hamers,et al.  Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda , 2013, Eur. J. Oper. Res..

[23]  Ulrik Brandes,et al.  Stars, neighborhood inclusion and network centrality , 2015 .

[24]  Stephen P. Borgatti,et al.  Centrality and network flow , 2005, Soc. Networks.

[25]  Vito Fragnelli,et al.  Using coalitional games on biological networks to measure centrality and power of genes , 2010, Bioinform..

[26]  Nicholas R. Jennings,et al.  Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality , 2014, J. Artif. Intell. Res..

[27]  Egon Wanke,et al.  Shapley Ratings in Brain Networks , 2007, Frontiers Neuroinformatics.

[28]  Simina Brânzei,et al.  Social Distance Games , 2011, IJCAI.

[29]  Talal Rahwan,et al.  Efficient algorithms for game-theoretic betweenness centrality , 2016, Artif. Intell..

[30]  Nicholas R. Jennings,et al.  Computational Analysis of Connectivity Games with Applications to the Investigation of Terrorist Networks , 2013, IJCAI.

[31]  Dario Rossi,et al.  The Green-Game: Striking a balance between QoS and energy saving , 2011, 2011 23rd International Teletraffic Congress (ITC).

[32]  Oskar Skibski,et al.  Algorithms for the shapley and myerson values in graph-restricted games , 2014, AAMAS.

[33]  Enrique González-Arangüena,et al.  Centrality in Directed Social Networks: A Game Theoretic Approach , 2010 .

[34]  J. S. Mateo.  The Shapley Value , 2012 .

[35]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

[36]  Xiaotie Deng,et al.  On the Complexity of Cooperative Solution Concepts , 1994, Math. Oper. Res..

[37]  Pradeep Dubey,et al.  Value Theory Without Efficiency , 1981, Math. Oper. Res..