Download This PaperImpact of Social Connectivity on Herding Behavior
16 Pages Posted: 5 Feb 2018 Last revised: 7 Oct 2018
Date Written: January 27, 2018
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 Erdos-Renyi random graph when the degree distribution of each vertex of the tree is Binomial and as the number of nodes grow 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 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 the groups with less social connections tend to herd more than the groups with more social connections.
Keywords: Informational Cascades, Social Learning, Networks
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