How Homophily Affects the Speed of Learning and Best Response Dynamics

Abstract

We examine how the speed of learning and best-response processes depends on homophily: the tendency of agents to associate disproportionately with those having similar traits. When agents' beliefs or behaviors are developed by averaging what they see among their neighbors, then convergence to a consensus is slowed by the presence of homophily, but is not influenced by network density. This is in stark contrast to the viral spread of a belief or behavior along shortest paths -a process whose speed is increasing in network density but does not depend on homophily. In deriving these results, we propose a new, general measure of homophily based on the relative frequencies of interactions among different groups.Keywords: networks, learning, diffusion, homophily, friendships, social networks, random graphs, convergence, speed of learning, speed of convergence, best response dynamics JEL Classification Numbers: D83, D85, I21, J15, Z13 * This is a change of title from "How Homophily Affects the Speed of Contagion, Best Response and Learning Dynamics." Jackson gratefully acknowledges financial support from the NSF under grants SES-0647867 and SES-SES-0961481. Golub gratefully acknowledges financial support from an NSF Graduate Research Fellowship, as well as the Clum, Holt, and Jaedicke fellowships at the Stanford Graduate School of Business. We also thank S. Nageeb Ali, Arun Chandrasekhar, Christoph Kuzmics, Carlos Lever, Yair Livne, Norma Olaizola Ortega, Lev Piarsky, Amin Saberi, Federico Valenciano, as well as Elhanan Helpman, Larry Katz, and the anonymous referees for comments and suggestions.

Heterogeneous network games: Conflicting preferences

“…As a consequence, although in a simplified static model, we study a richer setting where there is not one default action for all individuals, but each of them has preferences for one over the other. Note that this is different from homophily in the sense of Golub and Jackson (2010), where types control the probability of being linked, but do not make any difference in the preferences of individual players. In this sense, part of our contribution is that we obtain two different threshold functions, one for each identity of players for them to adopt the disliked action.…”

Social networks and environmental outcomes

“…It has been observed for various types of social relations, including friendships, marriage, and information sharing (12). Existing research on homophily shows that it can heavily influence the structure of social networks and their effects on people's lives (15)(16)(17)(18)(19)(20)(21)(22)(23). One of the most pervasive effects of homophily is that it can cause social networks to become highly clustered (13,21,24).…”

Exploring the Characteristics of Innovation Adoption in Social Networks: Structure, Homophily, and Strategy

“…Also, a(t) is the vector consisting of a i (t), i = 1,2,…,n. According to the results on Markov chains [33], as long as the network is connected, the process will convergence to a limit, which is summarized to the following Theorem 1 [29]: Theorem 1. If the network is connected, then T t convergences to a limit T ∞ such that…”

“…It is noted that the above Theorem 2 only gives a sufficient condition. Accordingly, we do not make q larger than lnN in the following simulation analysis, which is for two reasons: (1) the situation of q larger than (lnN)/N has been studied sufficiently since it has had analytical solutions (see also Golub and Jackson [29]); (2) Even if q is not larger than (lnN)/N, the updating process in the context of random network may also be convergent. As a result, we make N as 500 and q as 4 in the following simulation analysis, where 4 is smaller than ln (500).…”

“…As a result, this paper provides some new insights in the field of innovation adoption with network externalities. Admittedly, some papers such as the famous one by Golub and Jackson [29] have the similar setup as ours, since the two papers both adopt the definition of homophily and updating rules to analyze the agents' behaviors. However, the two updating rules shown in the two papers are heterogeneous: the paper done by Golub and Jackson adopts the average-based updating process, while our paper introduces two parameters to reflect the different updating efficiencies of different groups segregated according to the definition of homophily.…”