Communication dynamics in endogenous social networks

We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state (of the world) determines which action has higher payoff. Agents decide which agents to form a communication link with incurring the associated cost and receive a private signal correlated with the underlying state. They then exchange information over the induced communication network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking the correct action converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from “information hubs”, which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication is not always optimal, when the communication network induces asymptotic learning (in a large society), truthful communication is an ɛ-equilibrium. We then provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Our result shows that societies with too many and sufficiently large social cliques do not induce asymptotic learning, because each social clique would have sufficient information by itself, making communication with others relatively unattractive. Asymptotic learning results if social cliques are neither too numerous nor too large, in which case communication across cliques is encouraged. Finally, we show how these results can be applied to several commonly studied random graph models, such as preferential attachment and Erdős-Renyi graphs.