Forming k coalitions and facilitating relationships in social networks

Abstract In this paper we relax two common assumptions that are made when studying coalition formation. The first is that any number of coalitions can be formed; the second is that any possible coalition can be formed. We study a model of coalition formation where the value depends on a social network and exactly k coalitions must be formed. Additionally, in this context we present a new problem for an organizer that would like to introduce members of the social network to each other in order to increase the social welfare or to stabilize a coalition structure. We show that, when the number of coalitions, k, is fixed and there are not many negative edges, it is possible to find the coalition structure that maximizes the social welfare in polynomial time. Furthermore, an organizer can efficiently find the optimal set of edges to add to the network, and we experimentally demonstrate the effectiveness of this approach. In addition, we show that in our setting even when k is fixed and there are not many negative edges, finding a member of the core is intractable. However, we provide a heuristic for efficiently finding a member of the core that also guarantees a social welfare within a factor of 1/2 of the optimal social welfare. We also show that checking whether a given coalition structure is a member of the core can be done in polynomial time. Finally, we consider the problem faced by an organizer who would like to add edges to the network in order to stabilize a specific coalition structure core: we show that this problem is intractable.

[1]  Dorit S. Hochbaum,et al.  A Polynomial Algorithm for the k-cut Problem for Fixed k , 1994, Math. Oper. Res..

[2]  Rami Puzis,et al.  Organization Mining Using Online Social Networks , 2013, ArXiv.

[3]  Nicholas R. Jennings,et al.  Coalitional stability in structured environments , 2012, AAMAS.

[4]  Michael R. Fellows,et al.  Cutting Up is Hard to Do: the Parameterized Complexity of k-Cut and Related Problems , 2003, CATS.

[5]  Onn Shehory,et al.  Coalition structure generation with worst case guarantees , 2022 .

[6]  Sarit Kraus,et al.  Forming coalitions and facilitating relationships for completing tasks in social networks , 2014, AAMAS.

[7]  Christos Faloutsos,et al.  Kronecker Graphs: An Approach to Modeling Networks , 2008, J. Mach. Learn. Res..

[8]  Martin Hoefer,et al.  Hedonic Coalition Formation in Networks , 2015, AAAI.

[9]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[10]  Shao Chin Sung,et al.  On core membership testing for hedonic coalition formation games , 2007, Oper. Res. Lett..

[11]  Luca Becchetti,et al.  Online team formation in social networks , 2012, WWW.

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

[13]  C. D. De Dreu,et al.  Task versus relationship conflict, team performance, and team member satisfaction: a meta-analysis. , 2003, The Journal of applied psychology.

[14]  Nicholas R. Jennings,et al.  Coalition Structure Generation over Graphs , 2012, J. Artif. Intell. Res..

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

[16]  Paul Harrenstein,et al.  Fractional Hedonic Games , 2014, AAMAS.

[17]  Jörg Rothe,et al.  The Cost of Stability in Coalitional Games , 2009, SAGT.

[18]  Felix Brandt,et al.  Optimal Partitions in Additively Separable Hedonic Games , 2011, IJCAI.

[19]  Morteza Zadimoghaddam,et al.  Optimal Coalition Structure Generation in Cooperative Graph Games , 2013, AAAI.

[20]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[21]  Bernhard Schölkopf,et al.  Structure and dynamics of information pathways in online media , 2012, WSDM.

[22]  Bernhard Schölkopf,et al.  Uncovering the Temporal Dynamics of Diffusion Networks , 2011, ICML.

[23]  Yingqian Zhang,et al.  Multiagent task allocation in social networks , 2011, Autonomous Agents and Multi-Agent Systems.

[24]  Jeffrey S. Rosenschein,et al.  Subsidies, Stability, and Restricted Cooperation in Coalitional Games , 2011, IJCAI.

[25]  Zhu Han,et al.  A selfish approach to coalition formation among unmanned air vehicles in wireless networks , 2009, 2009 International Conference on Game Theory for Networks.

[26]  Laura Sanità,et al.  Stabilizing network bargaining games by blocking players , 2018, Math. Program..

[27]  Eyal Winter,et al.  Stability and Segregation in Group Formation , 2002, Games Econ. Behav..

[28]  Jochen Könemann,et al.  Network Bargaining: Using Approximate Blocking Sets to Stabilize Unstable Instances , 2012, Theory of Computing Systems.

[29]  Marie desJardins,et al.  Agent-organized networks for dynamic team formation , 2005, AAMAS '05.

[30]  Jeffrey S. Rosenschein,et al.  Coalitional skill games , 2008, AAMAS.

[31]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[32]  Giovanni Rinaldi,et al.  Easy and difficult objective functions for max cut , 2003, Math. Program..

[33]  Sarit Kraus,et al.  Solving coalitional resource games , 2010, Artif. Intell..

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

[35]  Laurie R. Weingart,et al.  TASK VERSUS RELATIONSHIP CONFLICT: A META-ANALYSIS. , 2002 .

[36]  Gabriel Kliot,et al.  Streaming graph partitioning for large distributed graphs , 2012, KDD.

[37]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[38]  Éva Tardos,et al.  Balanced outcomes in social exchange networks , 2008, STOC.

[39]  Simina Brânzei,et al.  Coalitional affinity games , 2009, AAMAS.