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The Diplomat’s Dilemma: Maximal Power for Minimal Effort in Social Networks

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Adaptive Networks

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social networks there is a cost of maintaining social ties. This leads to a situation (that can occur in the professional social networks of executives, lobbyists, diplomats and so on) where agents have the conflicting objectives of aiming for centrality while simultaneously keeping the degree low. We investigate this situation in an adaptive network-evolution model where agents optimize their positions in the network following individual strategies, and using only local information. The strategies are also optimized, based on the success of the agent and its neighbors. We measure and describe the time evolution of the network and the agents’ strategies.

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References

  1. Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–98

    Article  Google Scholar 

  2. Axelrod R (1984) The Evolution of Cooperation. Basic Books, New York.

    Google Scholar 

  3. Bala V, Goyal S (2000) A noncooperative model of network formation. Econometrica 68:1181–1229

    Article  MATH  MathSciNet  Google Scholar 

  4. Barrat A, Weigt M (2000) On the properties of small-world network models. Eur Phys J B 13:547–560

    Article  Google Scholar 

  5. Dorogovtsev SN, Mendes JFF (2003) Evolution of Networks: From Biological Nets to the Internet and WWW . Oxford University Press, Oxford

    Google Scholar 

  6. Ehrhardt G, Marsili M, Vega-Redondo F (2006) Diffusion and growth in an evolving network. Int J Game Theory 34:383–397

    Article  MATH  MathSciNet  Google Scholar 

  7. Erdős P, Rényi A (1959) On random graphs I. Publ Math Debrecen 6:290–297

    MathSciNet  Google Scholar 

  8. Gila S, Zanette DH (2006) Coevolution of agents and networks: Opinion spreading and community disconnection. Phys¡??¿ Lett¡??¿ A 356:89–94

    Article  Google Scholar 

  9. Gross T, Blasius B (2008) Adaptive coevolutionary networks: a review. J Roy Soc Interface 5:259–271

    Article  Google Scholar 

  10. Holland PW, Leinhardt S (1972) Some evidence on the transitivity of positive interpersonal sentiment. Am J Sociol 72:1205–1209

    Article  Google Scholar 

  11. Holme P, Ghoshal G (2006) Dynamics of networking agents competing for high centrality and low degree. Phys Rev Lett 96:098701

    Article  Google Scholar 

  12. Holme P, Newman MEJ (2006) Nonequilibrium phase transition in the coevolution of networks and opinions. Phys Rev E 74:056108

    Article  Google Scholar 

  13. Holme P, Zhao J (2007) Exploring the assortativity-clustering space of a network’s degree sequence. Phys Rev E 75:046111

    Article  Google Scholar 

  14. Jackson MO, Wolinsky A (1996) A strategic model of social and economic networks. J Eco Theory 71:44–74

    Article  MATH  MathSciNet  Google Scholar 

  15. Kahneman D (2003) Maps of bounded rationality: psychology for behavioral economics. The Am Eco Rev 93:1449–1475

    Article  Google Scholar 

  16. Knoke D (1990) Political Networks: The Structural Perspective. Cambridge University Press, Cambridge

    Google Scholar 

  17. Lindgren K, Nordahl MG (1994) Evolutionarycs of spatial games. Physica D 75:292–309

    Google Scholar 

  18. Nakao K (1990) Distribution of measures of centrality: Enumerated distributions of freeman’s graph centrality measures. Connections 13:10–22

    Google Scholar 

  19. Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256

    Article  MATH  MathSciNet  Google Scholar 

  20. Nowak M, Sigmund K (1992) A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner’s dilemma game. Nature 364:56–58

    Google Scholar 

  21. Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359:826–829

    Article  Google Scholar 

  22. Rosvall M, Sneppen K (2003) Modelling dynamics of information networks. Phys Rev Lett 91:178701

    Article  Google Scholar 

  23. Rosvall M, Sneppen K (2006) Modeling self-organization of communication and topology in social networks. Phys Rev E 74:016108

    Article  MathSciNet  Google Scholar 

  24. Sabidussi G (1966) The centrality index of a graph. Psychometrika 31:581–603

    Article  MATH  MathSciNet  Google Scholar 

  25. van Valen LM (1973) A new evolutionary law. Evol Theory 1:1–30

    Google Scholar 

  26. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442

    Article  Google Scholar 

  27. Weber M (1947) The Theory of Social and Economic Organization. Oxford University Press, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Umeå University, 90187, Umeå, Sweden

    Petter Holme

  2. Department of Physics, Michigan Center for Theoretical Physics, 48109, Ann Arbor, MI, USA

    Gourab Ghoshal

Authors
  1. Petter Holme
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  2. Gourab Ghoshal
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Corresponding author

Correspondence to Petter Holme .

Editor information

Editors and Affiliations

  1. MPI für Physik Komplexer Systeme, Nöthnitzer Str. 38, Dresden, 01187, Germany

    Thilo Gross

  2. Binghamton University, State University of New York, Binghamton, 13902-6000, U.S.A.

    Hiroki Sayama

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© 2009 Springer-Verlag Berlin Heidelberg

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Holme, P., Ghoshal, G. (2009). The Diplomat’s Dilemma: Maximal Power for Minimal Effort in Social Networks. In: Gross, T., Sayama, H. (eds) Adaptive Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01284-6_13

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  • DOI: https://doi.org/10.1007/978-3-642-01284-6_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01283-9

  • Online ISBN: 978-3-642-01284-6

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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