Top

Dynamic Games and Applications

Published in:

04-01-2020

Signed Network Formation Games and Clustering Balance

Authors: Pedro Cisneros-Velarde, Francesco Bullo

Published in: Dynamic Games and Applications | Issue 4/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We propose a signed network formation game, in which pairs of individuals strategically change the signs of the edges in a complete network. These individuals are members of a social network who strategically reduce cognitive dissonances by changing their interpersonal appraisals. We characterize the best-response dynamics for this game and prove that its implementation can dynamically drive the network to a sociologically meaningful sign configuration called clustering balance. In this configuration, agents in the social network form one or more clusters that have positive relationships among their members but negative relationships among members of other clusters. In the past, various researchers in the fields of psycho-sociology, political science, and physics have looked at models that explain the generation of up to two clusters. Our work contributes to these fields by proposing a simple model that generates a broader class of signed networks.

next article Price Dynamics for Electricity in Smart Grid Via Mean-Field-Type Games

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Given the action profile \(a=(a_{ij})\), we use the notation \((a'_{ij},a_{-ij})\) to denote a new action profile resulting from only changing the action of player \(\{i,j\}\) by \(a'_{ij}\) in a.

Antal T, Krapivsky PL, Redner S (2005) Dynamics of social balance on networks. Phys Rev E 72(3):036121. https://doi.org/10.1103/PhysRevE.72.036121MathSciNetCrossRef

Antal T, Krapivsky PL, Redner S (2006) Social balance on networks: the dynamics of friendship and enmity. Physica D 224(1):130–136. https://doi.org/10.1016/j.physd.2006.09.028MathSciNetCrossRefMATH

Calvó-Armengol A, İlkılıç R (2009) Pairwise-stability and Nash equilibria in network formation. Int J Game Theory 38(1):51–79. https://doi.org/10.1007/s00182-008-0140-7MathSciNetCrossRefMATH

Cisneros-Velarde P, Friedkin NE, Proskurnikov AV, Bullo F (Sept 2019) Structural balance via gradient flows over signed graphs. arXiv:1909.11281.pdf

Davis JA (1967) Clustering and structural balance in graphs. Hum Relat 20(2):181–187. https://doi.org/10.1177/001872676702000206CrossRef

Festinger L (1957) A theory of cognitive dissonance. Stanford University Press, Stanford

Grimmett G, Stirzaker D (2001) Probability and random processes. Oxford University Press, OxfordMATH

Heider F (1944) Social perception and phenomenal causality. Psychol Rev 51(6):358–374. https://doi.org/10.1037/h0055425CrossRef

Heider F (1946) Attitudes and cognitive organization. J Psychol 21(1):107–112. https://doi.org/10.1080/00223980.1946.9917275CrossRef

10.

Hiller T (2017) Friends and enemies: a model of signed network formation. Theor Econ 12(3):1057–1087. https://doi.org/10.3982/TE1937MathSciNetCrossRefMATH

11.

Huang H, Tang J, Liu L, Luo J, Fu X (2015) Triadic closure pattern analysis and prediction in social networks. IEEE Trans Knowl Data Eng 27(12):3374–3389. https://doi.org/10.1109/TKDE.2015.2453956CrossRef

12.

Jackson MO (2005) A survey of models of network formation: stability and efficiency. In: Demange G, Wooders M (eds) Group formation in economics: networks, clubs and coalitions. Cambridge University Press, Cambridge. https://web.stanford.edu/~jacksonm/netsurv.pdf

13.

Jackson MO, Nei S (2015) Networks of military alliances, wars, and international trade. Proc Natl Acad Sci 112(50):15277–15284. https://doi.org/10.1073/pnas.1520970112CrossRef

14.

Jackson MO, Watts A (2002) The evolution of social and economic networks. J Econ Theory 106(2):265–295. https://doi.org/10.1006/jeth.2001.2903MathSciNetCrossRefMATH

15.

Jia P, Friedkin NE, Bullo F (2016) The coevolution of appraisal and influence networks leads to structural balance. IEEE Trans Netw Sci Eng 3(4):286–298. https://doi.org/10.1109/TNSE.2016.2600058MathSciNetCrossRef

16.

Johnsen EC (1989) The micro–macro connection: exact structure and process. In: Roberts F (ed) Applications of combinatorics and graph theory to the biological and social sciences. Springer, Berlin, pp 169–201. https://doi.org/10.1007/978-1-4684-6381-1_7. ISBN 978-1-4684-6383-5

17.

Konig MD, Rohner D, Thoenig M, Zilibotti F (2017) Networks in conflict: theory and evidence from the great war of Africa. Econometrica 85(4):1093–1132. https://doi.org/10.3982/ECTA13117MathSciNetCrossRefMATH

18.

Kułakowski K, Gawroński P, Gronek P (2005) The Heider balance: a continuous approach. Int J Mod Phys C 16(05):707–716. https://doi.org/10.1142/S012918310500742XCrossRefMATH

19.

Leskovec J, Huttenlocher D, Kleinberg J (2010) Signed networks in social media. In: International conference on human factors in computing systems, Atlanta, pp 1361–1370. https://doi.org/10.1145/1753326.1753532

20.

Malekzadeh M, Fazli M, Jalaly Khalidabadi P, Rabiee HR, Safari MA (Aug 2011) Social balance and signed network formation games. In: Proceedings of 5th KDD workshop on social network analysis (SNA-KDD), San Diego

21.

Marvel SA, Strogatz SH, Kleinberg JM (2009) Energy landscape of social balance. Phys Rev Lett 103:198701. https://doi.org/10.1103/PhysRevLett.103.198701CrossRef

22.

Marvel SA, Kleinberg J, Kleinberg RD, Strogatz SH (2011) Continuous-time model of structural balance. Proc Natl Acad Sci 108(5):1771–1776. https://doi.org/10.1073/pnas.1013213108CrossRef

23.

Mei W, Cisneros-Velarde P, Chen G, Friedkin NE, Bullo F (Oct 2017) Dynamic social balance and convergent appraisals via homophily and influence mechanisms. Automatica. arXiv:1710.09498.pdf

24.

Radicchi F, Vilone D, Yoon S, Meyer-Ortmanns H (2007) Social balance as a satisfiability problem of computer science. Phys Rev E 75:026106. https://doi.org/10.1103/PhysRevE.75.026106MathSciNetCrossRef

25.

Ric F (2015) Social cognition. In: Wright JD (ed) International encyclopedia of the social and behavioral sciences, 2nd edn. Elsevier, London, pp 204–209. https://doi.org/10.1016/B978-0-08-097086-8.24044-0. ISBN 9780080970875

26.

Traag VA, Dooren PV, Leenheer PD (2013) Dynamical models explaining social balance and evolution of cooperation. PLoS ONE 8(4):e60063. https://doi.org/10.1371/journal.pone.0060063CrossRef

27.

van de Rijt A (2011) The micro–macro link for the theory of structural balance. J Math Sociol 35(1–3):94–113. https://doi.org/10.1080/0022250X.2010.532262MathSciNetCrossRefMATH

28.

Zheng X, Zeng D, Wang F-Y (2015) Social balance in signed networks. Inf Syst Front 17(5):1077–1095. https://doi.org/10.1007/s10796-014-9483-8CrossRef

Title: Signed Network Formation Games and Clustering Balance
Authors: Pedro Cisneros-Velarde
Francesco Bullo
Publication date: 04-01-2020
Publisher: Springer US
Published in: Dynamic Games and Applications / Issue 4/2020
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-019-00346-8

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 4/2020

Cooperative Dynamic Games with Durable Controls: Theory and Application

A Stackelberg Game of Backward Stochastic Differential Equations with Applications

Power Markets with Information-Aware Self-scheduling Electric Vehicles

Stationary Equilibria of Mean Field Games with Finite State and Action Space

Optimal Strategies in Zero-Sum Repeated Games with Incomplete Information: The Dependent Case

A Turn-Based Game Related to the Last-Success-Problem

Premium Partner