Polarization in Communication Games

Abstract

In this dissertation I explore the incentives and ability of the agent with informational superiority to polarize her rational audience. I explore this question in the context of strategic communication games. The first chapter introduces the problem of explaining polarization without diverting from rational agents assumption and describes the mechanism using which this could be done.In the second chapter I extend the standard cheap talk model in a minimal way to capture the possible incentives of polarization. For this, I add one receiver and one binary payoff irrelevant state variable to the standard model. In contrast to payoff relevant variable, receivers have different beliefs about payoff irrelevant one. Besides the equilibria of standard model, my extension admits continuum of new equilibria and expands the set of sender's equilibrium payoffs. I characterize a set of polar equilibria and prove that this set of equilibria spans the sender's payoff space. I also show that in these equilibria, receivers are polarized. Namely, their posterior beliefs are ordered with first-order stochastic dominance. Moreover, when ex-ante receivers disagreement rises, then there is more scope for manipulation by the sender. Specifically, the set of aggregate actions and sender payoffs that can be supported in equilibrium expands as the receivers' posterior beliefs diverge. We show that even slight disagreement about payoff irrelevant state is enough for influential equilibrium to exist for any bias level. When disagreement increases, the equilibria set expands, and the bias threshold above which there are no multiaction equilibria also increases. In the third chapter which is co-authored with Axel Anderson we consider a Bayesian persuasion game between a single sender and two receivers. The sender's payoff is monotone in the receivers' beliefs about the payoff relevant state. All agents share a common prior about this state. However, we allow disagreement about a payoff irrelevant state, a binary variable that enters no utility functions. When all agents have the same prior beliefs about payoff irrelevant state, then the model is a version of Kamenica and Gentzkow (2011). However disparate priors significantly change the results. In particular, it is no longer true that sender fully conceals the state when her payoff is concave in beliefs and fully reveals the state when payoff is convex in beliefs. In fact, if the sender's payoff is differentiable and strictly monotone, then even slight disagreement on the payoff irrelevant state guarantees that the sender can strictly increase her payoff by using an informative signal. Moreover, the sender's payoff is strictly increasing in the prior disagreement between the receivers. Given extreme prior disagreement between the receivers, we show that persuasion induces significant belief polarization for two general classes of payoff functions. Specifically, if the sender's payoff is biconcave and submodular, then signals are strongly polarizing; namely, the signal that makes receiver 1 most confident that the payoff relevant state is 1 makes receiver 2 least confident that the payoff relevant state is 1, and the signal that makes receiver 1 second most confident the payoff relevant state is 1 makes receiver 2 second most confident the payoff relevant state is 1, etc. If the sender's payoff biconvex, then the sender chooses a message service with three signals, and receiver's beliefs are diametrically opposed for two of the three signals.