Benjamin Golub

Papers

A Network Centrality Approach to Coalitionally Stable Outcomes in Public Goods Games (with Matthew Elliott) 

Eigenvector centrality can be used to find a scheme for providing a public good (such as pollution reduction) in such a way that no coalition of countries has an incentive to deviate — without parametric assumptions on utility functions. [ More]

We study games in which each player simultaneously exerts costly effort that provides different benefits to each other player. The goal is to find and describe effort profiles that are immune to coordinated coalitional deviations when such a game is played repeatedly. Formally, these effort profiles are the ones that can be sustained in a strong Nash equilibrium of the repeated game. We introduce a class of effort profiles that are called centrality-stable. These are characterized by a network centrality condition: agent i's contribution (defined as effort level times marginal cost) is equal to a weighted sum of the contributions of those who help i; the weight on j's contribution measures the marginal benefit j's effort provides to i. Under certain assumptions (mainly concavity of utility functions), centrality-stable profiles exist, are Pareto-efficient, and any such profile is sustainable in a coalitionally robust equilibrium of the repeated game. Centrality-stable profiles also have an alternative definition: they are those at which all agents are first-order indifferent to scaling all efforts by a factor near 1. This single condition rules out all profitable coalitional deviations. The results are obtained without parametric assumptions, using the theory of general equilibrium and its relation to the core, along with the Perron-Frobenius spectral theory of nonnegative matrices. When agents are uncertain about each other's utility functions but can verify marginal costs and benefits at an implemented effort profile, then the centrality-stable profiles are the only ones that are immune to manipulation through misreporting of preferences.

First version: September, 2011. Current version:December 10, 2010. Working paper.

How Homophily Affects Diffusion and Learning in Networks (with Matthew O. Jackson) 

Accepted subject to minor revisions, Quarterly Journal of Economics.

How 'fact' and 'opinion' transmission are affected by segregation patterns in networks.  

[ More] [Slides]

We examine how diffusion and learning processes are influenced by network properties, focusing on density and homophily  — the tendency of agents to associate disproportionately with those sharing similar traits. Homophily does not affect the speed of diffusions that travel along shortest paths; their rate is determined only by the size of the society and the number of links per agent. In contrast, homophily substantially slows learning based on repeated averaging of neighbors' information, as in the DeGroot model of consensus formation. Indeed, the latter process is strongly affected by homophily but completely independent of connection density beyond a low threshold. Our analysis shows that changing a network can have widely different effects on information flow depending on the details of the transmission process and we provide general tools for analyzing such changes.

First version: November 24, 2008. Current version:September 10, 2010. Submitted.

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.

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.

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. 

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: September 26, 2010. Submitted.

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]

Network centrality measures based on eigenvectors are related to investment decisions, transmission of information, and local public goods provision. We study how the centrality of each member of a society changes when initially disconnected groups begin interacting with each other. We find that 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 with a low-centrality member of another, the latter's group will have a proportionally larger share of the total centrality. We also find that agents who form the intergroup link, the ``bridge agents'', become relatively more central within their own groups, while all other members keep a stable share of centrality relative to their groups.

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.