We study learning in a setting where agents receive independent noisy signals about the true value of a variable and then communicate in a network. They naïvely update beliefs by repeatedly taking weighted averages of neighbors' opinions. We show that all opinions in a large society converge to the truth if and only if the influence of the most influential agent vanishes as the society grows. We also identify obstructions to this, including prominent groups, and provide structural conditions on the network ensuring efficient learning. Whether agents converge to the truth is unrelated to how quickly consensus is approached. (JEL D83, D85, Z13)

Globalization brings with it increased financial interdependencies among many kinds of organizations-governments, central banks, investment banks, firms, etc.-that hold each other's shares, debts, and other obligations. Such interdependencies can lead to cascading defaults and failures, which are often avoided through massive bailouts of institutions deemed "too big to fail." Recent examples include the US government's interventions in AIG, Fannie Mae, Freddie Mac, and General Motors; and the European Commission's interventions in Greece and Spain. Although such bailouts circumvent the widespread failures that were more prevalent in the nineteenth and early twentieth centuries, they emphasize the need to study the risks created by a network of interdependencies. Understanding these risks is crucial to designing incentives and regulatory responses which defuse cascades before they are imminent.In this paper we develop a general model that produces new insights regarding financial contagions and cascades of failures among organizations linked through a network of financial interdependencies. Organizations' values depend on each other-e.g., through cross-holdings of shares, debt, or other liabilities. If an

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.

Globalization brings with it increased financial interdependencies among many kinds of organizations-governments, central banks, investment banks, firms, etc.-that hold each other's shares, debts, and other obligations. Such interdependencies can lead to cascading defaults and failures, which are often avoided through massive bailouts of institutions deemed "too big to fail." Recent examples include the US government's interventions in AIG, Fannie Mae, Freddie Mac, and General Motors; and the European Commission's interventions in Greece and Spain. Although such bailouts circumvent the widespread failures that were more prevalent in the nineteenth and early twentieth centuries, they emphasize the need to study the risks created by a network of interdependencies. Understanding these risks is crucial to designing incentives and regulatory responses which defuse cascades before they are imminent.In this paper we develop a general model that produces new insights regarding financial contagions and cascades of failures among organizations linked through a network of financial interdependencies. Organizations' values depend on each other-e.g., through cross-holdings of shares, debt, or other liabilities. If an

We study games in which a network mediates strategic spillovers and externalities among the players. How does a planner optimally target interventions that change individuals' private returns to investment? We analyze this question by decomposing any intervention into orthogonal principal components, which are determined by the network and are ordered according to their associated eigenvalues. There is a close connection between the nature of spillovers and the representation of various principal components in the optimal intervention. In games of strategic complements (substitutes), interventions place more weight on the top (bottom) principal components, which reflect more global (local) network structure. For large budgets, optimal interventions are simple—they essentially involve only a single principal component.