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Search in the Formation of Large Networks: How Random are Socially Generated Networks?

Author

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  • Matthew O. Jackson

    (Caltech)

  • Brian W. Rogers

    (Caltech)

Abstract

We present a model of network formation where entering nodes find other nodes to link to both completely at random and through search of the neighborhoods of these randomly met nodes. We show that this model exhibits the full spectrum of features that have been found to characterize large socially generated networks. Moreover, we derive the distribution of degree (number of links) across nodes, and show that while the upper tail of the distribution is approximately ``scale- free,'' the lower tail may exhibit substantial curvature, just as in observed networks. We then fit the model to data from six networks. Besides offering a close fit of these diverse networks, the model allows us to impute the relative importance of search versus random attachment in link formation. We find that the fitted ratio of random meetings to search-based meetings varies dramatically across these applications. Finally, we show that as this random/search ratio varies, the resulting degree distributions can be completely ordered in the sense of second order stochastic dominance. This allows us to infer how the relative randomness in the formation process affects average utility in the network.

Suggested Citation

  • Matthew O. Jackson & Brian W. Rogers, 2005. "Search in the Formation of Large Networks: How Random are Socially Generated Networks?," Game Theory and Information 0503005, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0503005
    Note: Type of Document - pdf; pages: 44
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0503/0503005.pdf
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    References listed on IDEAS

    as
    1. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
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    3. Matthew O. Jackson & Brian W. Rogers, 2005. "The Economics of Small Worlds," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 617-627, 04/05.
    4. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    5. Sanjeev Goyal & Marco J. van der Leij & José Luis Moraga-Gonzalez, 2006. "Economics: An Emerging Small World," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 403-432, April.
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    7. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    8. Gabrielle Demange & Wooders Myrna, 2005. "Group Formation in Economics: Networks, Clubs and Coalitions," Post-Print halshs-00576778, HAL.
    9. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
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    Citations

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    Cited by:

    1. Yannis M. Ioannides, 2005. "Random Graphs and Social Networks: An Economics Perspective," Discussion Papers Series, Department of Economics, Tufts University 0518, Department of Economics, Tufts University.
    2. Gabrielle Demange, 2011. "On the influence of rankings," PSE Working Papers halshs-00589657, HAL.
    3. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 51-79, March.
    4. Pin, Paolo, 2011. "Eight degrees of separation," Research in Economics, Elsevier, vol. 65(3), pages 259-270, September.
    5. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, Oxford University Press, vol. 121(2), pages 461-504.
    6. Goeree, Jacob K. & Riedl, Arno & Ule, Aljaz, 2009. "In search of stars: Network formation among heterogeneous agents," Games and Economic Behavior, Elsevier, vol. 67(2), pages 445-466, November.
    7. Kleimeier, Stefanie & Sander, Harald, 2006. "Regional versus global integration of euro-zone retail banking markets: Understanding the recent evidence from price-based integration measures," The Quarterly Review of Economics and Finance, Elsevier, vol. 46(3), pages 353-368, July.
    8. Calvó-Armengol, Antoni & Patacchini, Eleonora & Zenou, Yves, 2005. "Peer Effects and Social Networks in Education and Crime," Working Paper Series 645, Research Institute of Industrial Economics.

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    More about this item

    Keywords

    Networks; Network Formation; Power Laws; Scale-Free Networks; Small Worlds; Search;
    All these keywords.

    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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