Essays on Social Learning and Networks

Citation

Martynov, Vadim Vadimovich (2020) Essays on Social Learning and Networks. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0m03-b330. https://resolver.caltech.edu/CaltechTHESIS:05122020-180653707

Abstract

This thesis offers a contribution to the study of Social Learning and Networks. It studies information aggregation and its effect on individual's actions (Chapter 2, 3) and social network (Chapter 4).

Chapter 2, co-authored with Omer Tamuz and Wade Hann-Caruthers, studies how quickly does the public belief converge to its true value when agents are able to observe actions of their predecessors. In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is unbounded, it is known that agents converge to the correct action and correct belief. We study how quickly convergence occurs, and show that it happens more slowly than it does when agents observe signals. However, we also show that the speed of learning from actions can be arbitrarily close to the speed of learning from signals. In particular, the expected time until the agents stop taking the wrong action can be either finite or infinite, depending on the private signal distribution. In the canonical case of Gaussian private signals, we calculate the speed of convergence precisely, and show explicitly that, in this case, learning from actions is significantly slower than learning from signals.

In Chapter 3, I investigate how social planning can reduce the inefficiencies of social learning, stemming from herding and informational cascades. A social planner is introduced to the classical sequential social learning model. She can tax or subsidize players' actions in order to maximize social welfare, a discounted sum of agents' utilities. We solve or accurately approximate the expected utility of the social planner and the optimal pricing strategy for various signal distributions. In equilibrium, it is optimal to increase the price for the better action, causing a reduction in current agent's utility, but also a net gain, due to the information this action reveals. The addition of the social planner significantly improves social welfare and the asymptotic speed of learning.

Chapter 4 analyzes how different types of social connections between people shape their social networks. There are two possible types of ties between individuals, strong and weak, that differ in maintenance costs and reliability. A network formation game is played in which agents choose the number of ties of each type to maximize their chances of hearing about a new job opportunity. We find that in equilibrium, people maintain both types of connections, which was not explained in previous theoretical models. Furthermore, in the socially optimal symmetric network, there are more strong ties than in the equilibrium one.

Thesis Files