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Endogenous control of DeGroot belief learning

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Abstract

Our focus in this paper is to study a specific type of imitative behavior in the framework of non-Bayesian models, and to endow it with an endogenous control mechanism aimed at modeling a leader-following behavior. We show how an agent’s assertion of endogenous control in a social network is learned dynamically by the other agents in the course of their interactions. We develop variants of the DeGroot algorithm which we call BLIFT to illustrate two scenarios which lead to completely different situations. We illustrate how control could be related to changes in the social influence weights and how its manipulation could lead to a general consensus or homophily in a network. We show the convergence of the two algorithms and analyze their theoretical properties. We construct synthetic examples to illustrate our two methods.

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Notes

  1. In its Markov chain analog the T matrix is said to be irreducible and aperiodic if it represents a strongly connected network where there is a ‘path’ connecting every agent to every other agent, and the gcd of paths is 1, implying that idiosyncratic weights are non-zero. Under these conditions the beliefs converge to a consensus in the DeGroot cycle (Eugene 1981).

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Acknowledgments

This work is supported by Ecometrix Research. The authors thank an anonymous reviewer for critical comments and helpful suggestion for improvement of the presentation.

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  1. Ecometrix Research, Bangalore, India

    Sridhar Mandyam & Usha Sridhar

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  1. Sridhar Mandyam
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  2. Usha Sridhar
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Correspondence to Usha Sridhar.

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Mandyam, S., Sridhar, U. Endogenous control of DeGroot belief learning. Soc. Netw. Anal. Min. 3, 803–812 (2013). https://doi.org/10.1007/s13278-013-0094-z

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