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Impact of Social Connectivity on Herding Behavior

  • Deepanshu VasalEmail author
Conference paper
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)

Abstract

Information cascades have been studied in the literature where myopic selfish users sequentially appear and make a decision to buy a product based on their private observation about the value of the product and actions of their predecessors. Bikhchandani et. al (1992) and Banerjee (1992) introduced such a model and showed that after a finite time, almost surely, users discard their private information and herd on an action asymptotically. In this paper, we study a generalization of that model where we assume users are connected through a random tree, which locally acts as an approximation for Erdös–Rényi random graph when the degree distribution of each vertex of the tree is binomial and as the number of nodes grows large. We show that informational cascades on such tree-structured networks may be analyzed by studying the extinction probability of a certain branching process. We use the theory of multi-type Galton–Watson branching process and calculate the probability of the tree network falling into a cascade. More specifically, we find conditions when this probability is strictly smaller than 1 that are in terms of the degree distributions of the vertices in the tree. Our results indicate that groups that are less tightly knit, i.e., have lesser connection probability (and as a result have lesser diversity of thought), tend to herd more than the groups that have more social connections.

Keywords

Information cascades Multi-type Galton–Watson process Social learning 

Notes

Acknowledgements

The author would like to thank Varun Jog for interesting discussions and anonymous reviewers for the feedback.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of TexasAustinUSA

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