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Journal of Systems Science and Complexity

, Volume 27, Issue 3, pp 581–593 | Cite as

Social learning with time-varying weights

  • Qipeng LiuEmail author
  • Aili Fang
  • Lin Wang
  • Xiaofan Wang
Article

Abstract

This paper investigates a non-Bayesian social learning model, in which each individual updates her beliefs based on private signals as well as her neighbors’ beliefs. The private signal is involved in the updating process through Bayes’ rule, and the neighbors’ beliefs are embodied in through a weighted average form, where the weights are time-varying. The authors prove that agents eventually have correct forecasts for upcoming signals, and all the beliefs of agents reach a consensus. In addition, if there exists no state that is observationally equivalent to the true state from the point of view of all agents, the authors show that the consensus belief of the whole group eventually reflects the true state.

Keywords

Consensus social learning social networks time-varying weights 

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References

  1. [1]
    Banerjee A, A simple model of herd behavior, The Quarterly Journal of Economics, 1992, 107(3): 797–817.CrossRefGoogle Scholar
  2. [2]
    Bikhchandani S, Hirshleifer D, and Welch I, A theory of fads, fashion, custom, and cultural change as informational cascades, The Journal of Political Economy, 1992, 100(5): 992–1026.CrossRefGoogle Scholar
  3. [3]
    Smith L and Sorensen P, Pathological outcomes of observational learning, Econometrica, 2000, 68(2): 371–398.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    Gale D and Kariv S, Bayesian learning in social networks, Games and Economic Behavior, 2003, 45(2): 329–346.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    Kagel J H and Roth A E, Handbook of Experimental Economics, Princeton University Press, Princeton, 1995.Google Scholar
  6. [6]
    Rabin M, Psychology and economics, Journal of Economics Literature, 1998, 36: 11–46.Google Scholar
  7. [7]
    DeGroot M H, Reaching a consensus, Journal of the American Statistical Association, 1974, 69(345): 118–121.CrossRefzbMATHGoogle Scholar
  8. [8]
    DeMarzo P M, Vayanos D, and Zwiebel J, Persuasion bias, social influence, and unidimensional opinions, The Quarterly Journal of Economics, 2003, 118(3): 909–968.CrossRefzbMATHGoogle Scholar
  9. [9]
    Golub B and Jackson M O, Naïve learning in social networks: Convergence, influence, and the wisdom of crowds, American Economic Journal: Microeconomics, 2010, 2(1): 112–149.Google Scholar
  10. [10]
    Jadbabaie A, Lin J, and Morse A, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automatic Control, 2003, 48(6): 988–1001.CrossRefMathSciNetGoogle Scholar
  11. [11]
    Olfati-Saber R and Murray R M, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automatic Control, 2004, 49(9): 1520–1533.CrossRefMathSciNetGoogle Scholar
  12. [12]
    Ren W and Beard R W, Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Automatic Control, 2005, 50(5): 655–661.CrossRefMathSciNetGoogle Scholar
  13. [13]
    Yu W, Chen G, Cao M, and Kurths J, Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Trans. Systems, Man, and Cybernetics-Part B, 2010, 40(3): 881–891.CrossRefGoogle Scholar
  14. [14]
    Jadbabaie A, Molavi P, Sandroni A, and Tahbaz-Salehi A, Non-Bayesian social learning, Games and Economic Behavior, 2012, 76(1): 210–225.CrossRefzbMATHMathSciNetGoogle Scholar
  15. [15]
    McPherson M, Smith-Lovin L, and Cook J M, Birds of a feather: Homophily in social networks, Annual Review of Sociology, 2001, 27: 415–444.CrossRefGoogle Scholar
  16. [16]
    Savage L J, The Foundations of Statistics, Wiley, New York, 1954.zbMATHGoogle Scholar
  17. [17]
    Seneta E, Non-Negative Matrices and Markov Chains, Springer, New York, 1981.CrossRefzbMATHGoogle Scholar
  18. [18]
    Meyer D C, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, 2000.CrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of AutomationShanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of ChinaShanghaiChina

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