Benjamin Golub

Papers

A Network Approach to Public Goods  (with Matthew Elliott) 

Perron eigenvalues are a natural way to measure whether an economic system is at an efficient point, and eigenvector centrality relates naturally to (Lindahl) market outcomes. We demonstrate these connections in a simple model of investment with externalities, without parametric assumptions. [ More]

We study settings where each agent can exert costly effort that creates nonrival, heterogeneous benefits for some of the others. For example, municipalities can forgo consumption to reduce pollution. How do the prospects for efficient cooperation depend on asymmetries in the effects of players' actions? We approach this question by analyzing a network that describes the marginal benefits agents can confer on one another. The first set of results explains how the largest eigenvalue of this network measures the marginal gains available from cooperating; as an application, we describe the players whose participation is essential to achieving any Pareto improvement on an inefficient status quo. Next, we examine mechanisms all of whose equilibria are Pareto efficient and individually rational; an outcome is called robust if it is an equilibrium outcome in every such mechanism. Robust outcomes exist and correspond to the Lindahl public goods solutions. The main result is a characterization of effort levels at these outcomes in terms of players' centralities in the benefits network. It entails that an outcome is robust if and only if agents contribute in proportion to how much they value the efforts of those who help them.

First version: November 2012. Current version: April 16, 2013. Working paper.

How Homophily Affects the Speed of Learning and Best-Response Dynamics (with Matthew O. Jackson) 

Quarterly Journal of Economics 127(3), August 2012.

Group-level segregation patterns in networks seriously slow convergence to consensus behavior when agents' choices are based on an average of neighbors' choices. When the process is a simple contagion, homophily doesn't matter.

[ More] [Pre-print version] [Slides]

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 (in contrast to other network processes that depend on shortest paths). In deriving these results, we propose a new, general measure of homophily based on the relative frequencies of interactions among different groups. An application to communication in a society before a vote shows how the time it takes for the vote to correctly aggregate information depends on the homophily and the initial information distribution.

First version: November 24, 2008. Revised: June 2012.

How Better Information Can Garble Experts' Advice  (with Matthew Elliott and Andrei Kirilenko) 

Do we get better advice as our experts get smarter? Two experts, who like to be right, make predictions about whether an event will occur based on private signals about its likelihood.  It is possible for both experts' information to improve unambiguously while the usefulness of their advice to any third party unambiguously decreases. [ More]

We model two experts who must make predictions about whether an event will occur or not. The experts receive private signals about the likelihood of the event occurring, and simultaneously make one of a finite set of possible predictions, corresponding to varying degrees of alarm. The information structure is commonly known among the experts and the recipients of the advice. Each expert's payoff depends on whether the event occurs, her prediction, and possibly the prediction of the competing expert. Our main result shows that when either or both experts receive uniformly more informative signals, their predictions can become unambiguously less informative. We call such information improvements perverse. Suppose a third party wishes to use the experts' recommendations to decide whether to take some costly preemptive action to mitigate a possible bad event. The third party would then trade off the costs of two kinds of mistakes: (i) failing to take action when the event will occur; and (ii) needlessly taking the action when the event will not occur. Regardless of how this third party trades off the associated costs, he will be worse off after a perverse information improvement. These perverse information improvements can occur when each expert's payoff is independent of the other expert's predictions and when the information improvement is due to a transfer of technology between the experts.

First version: November 21, 2010. Current version: June 11, 2012. Working paper.

Strategic Random Networks and Tipping Points in Network Formation  (with Yair Livne) 

If agents form networks in an environment of uncertainty, then arbitrarily small changes in economic parameters (such as costs and benefits of linking) can discontinuously change the properties of the equilibrium networks, especially efficiency. [ More]

Agents invest costly effort to socialize. Their effort levels determine the probabilities of relationships, which are valuable for their direct benefits and also because they lead to other relationships in a later stage of ``meeting friends of friends''. In contrast to many network formation models, there is fundamental uncertainty at the time of investment regarding which friendships will form. The equilibrium outcomes are random graphs, and we characterize how their density, connectedness, and other properties depend on the economic fundamentals. When the value of friends of friends is low, there are both sparse and thick equilibrium networks. But as soon as this value crosses a key threshold, the sparse equilibria disappear completely and only densely connected networks are possible. This transition mitigates an extreme inefficiency.

First version: April, 2010. Current version: November 2, 2010. Working paper.

Naive Learning in Social Networks and the Wisdom of Crowds (with Matthew O. Jackson)

American Economic Journal: Microeconomics, 2(1):112-149, February 2010.
In what networks do agents who learn very naively get the right answer? 

[ More] [Three-page version] [Slides]

We study learning and influence in a setting where agents receive independent noisy signals about the true value of a variable of interest and then communicate according to an arbitrary social network. The agents naively update their beliefs over time in a decentralized way by repeatedly taking weighted averages of their neighbors' opinions.  We identify conditions determining whether the beliefs of all agents in large societies converge to the true value of the variable, despite their naive updating.  We show that such convergence to truth obtains if and only if the influence of the most influential agent in the society is vanishing as the society grows. We identify obstructions which can prevent this, including the existence of prominent groups which receive a disproportionate share of attention. By ruling out such obstructions, we provide structural conditions on the social network that are sufficient for convergence to the truth. Finally, we discuss the speed of convergence and note that whether or not the society converges to truth is unrelated to how quickly a society's agents reach a consensus.

First version: January 14, 2007. Revised: April 17, 2009. 

Using Selection Bias to Explain the Observed Structure of Internet Diffusions (with Matthew O. Jackson) 

Proceedings of the National Academy of Sciences, 107(24):10833-10836, June 15, 2010.

David Liben-Nowell and Jon Kleinberg have observed that the reconstructed family trees of chain letter petitions are strangely tall and narrow. We show that this can be explained with selection and observation biases within a simple model. [ More] [PNAS blurb]

Recently, large data sets stored on the Internet have enabled the analysis of processes, such as large-scale diffusions of information, at new levels of detail. In a recent study, Liben-Nowell and Kleinberg ((2008) Proc Natl Acad Sci USA 105:4633-4638) observed that the flow of information on the Internet exhibits surprising patterns whereby a chain letter reaches its typical recipient through long paths of hundreds of intermediaries.  We show that a basic Galton-Watson epidemic model combined with the selection bias of observing only large diffusions suffices to explain the global patterns in the data.  This demonstrates that accounting for selection biases of which data we observe can radically change the estimation of classical diffusion processes.

First version: January 2010. Revised: May 24, 2010.

Does Homophily Predict Consensus Times? Testing a Model of Network Structure via a Dynamic Process  (with Matthew O. Jackson)

Forthcoming, Review of Network Economics.

Many random network models forget most of the details of a network, focusing on just a few dimensions of its structure. Can such models nevertheless make good predictions about how a process would run on real networks, in all their complexity? [ More]

We test theoretical results from Golub and Jackson (2012a), which are based on a random network model, regarding time to convergence of a learning/behavior-updating process. In particular, we see how well those theoretical results match the process when it is simulated on empirically observed high school friendship networks. This tests whether a parsimonious random network model mimics real-world networks with regard to predicting properties of a class of behavioral processes. It also tests whether our theoretical predictions on asymptotically large societies are accurate when applied to populations ranging from thirty to three thousand individuals. We find that the theoretical results account for more than half of the variation in convergence times on the real networks. We conclude that a simple multi-type random network model with types defined by simple observable attributes (age, sex, race) captures aspects of real networks that are relevant for a class of iterated updating processes.

First version: February 2012. Current version: August 15, 2012.

Network Structure and the Speed of Learning: Measuring Homophily Based on its Consequences (with Matthew O. Jackson)

Forthcoming, Annals of Economics and Statistics.

A simple measure of segregation in a network (in which less popular people matter more) predicts quite precisely how long convergence of beliefs will take under a naive process in which agents form their own beliefs by averaging those of their neighbors. [ More]

Homophily is the tendency of people to associate relatively more with those who are similar to them than with those who are not. In Golub and Jackson (2010a), we introduced degree-weighted homophily (DWH), a new measure of this phenomenon, and showed that it gives a lower bound on the time it takes for a certain natural best-reply or learning process operating in a social network to converge. Here we show that, in important settings, the DWH convergence bound does substantially better than previous bounds based on the Cheeger inequality. We also develop a new complementary upper bound on convergence time, tightening the relationship between DWH and updating processes on networks. In doing so, we suggest that DWH is a natural homophily measure because it tightly tracks a key consequence of homophily  — namely, slowdowns in updating processes.

First version: April 2010. Current version: March 11, 2011.

The Leverage of Weak Ties: How Linking Groups Affects Inequality  (with Carlos Lever) 

Arbitrarily weak bridges linking social groups can have arbitrarily large consequences for inequality. [ More]

Centrality measures based on eigenvectors are important in models of how networks affect investment decisions, the transmission of information, and the provision of local public goods. We fully characterize how the centrality of each member of a society changes when initially disconnected groups begin interacting with each other via a new bridging link. Arbitrarily weak intergroup connections can have arbitrarily large effects on the distribution of centrality. For instance, if a high-centrality member of one group begins interacting symmetrically with a low-centrality member of another, the latter group has the larger centrality in the combined network — in inverse proportion to the centrality of its emissary! We also find that agents who form the intergroup link, the ``bridge agents'', become relatively more central within their own groups, while other intragroup centrality ratios remain unchanged.

Current version: April 12, 2010. Working paper.

 

Firms, Queues, and Coffee Breaks: A Flow Model of Corporate Activity with Delays (with R. Preston McAfee)  

Review of Economic Design, 15(1), March 2011.
How and when to decentralize networked production — in a model that takes into account 'human' features of processing. [ More]

The multidivisional firm is modeled as a system of interconnected nodes that exchange continuous flows of projects of varying urgency and queue waiting tasks. The main innovation over existing models is that the rate at which waiting projects are taken into processing depends positively on both the availability of resources and the size of the queue, capturing a salient quality of human organizations. A transfer pricing scheme for decentralizing the system is presented, and conditions are given to determine which nodes can be operated autonomously. It is shown that a node can be managed separately from the rest of the system when all of the projects flowing through it are equally urgent.

First version: May 2006. Revised: September 22, 2009.

Stabilizing Brokerage (with Katherine Stovel and Eva Meyersson Milgrom) 

Proceedings of the National Academy of Sciences, 108(Suppl. 4):21326-21332, December 27, 2011.

Brokers facilitate transactions across gaps in social structure, and there are many reasons for their position to be unstable. Here, we take a look, from a sociological and an economic perspective, at what institutions stabilize brokerage. [ More]

A variety of social and economic arrangements exist to facilitate the exchange of goods, services, and information over gaps in social structure. Each of these arrangements bears some relationship to the idea of brokerage, but this brokerage is rarely like the pure and formal economic intermediation seen in some modern markets. Indeed, for reasons illuminated by existing sociological and economic models, brokerage is a fragile relationship. In this paper, we review the causes of instability in brokerage and identify three social mechanisms that can stabilize fragile brokerage relationships: social isolation, broker capture, and organizational grafting. Each of these mechanisms rests on the emergence or existence of supporting institutions. We suggest that organizational grafting may be the most stable and effective resolution to the tensions inherent in brokerage, but it is also the most institutionally demanding.