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Benjamin Golub

Publications and source records attributed to Benjamin Golub.

At least 19 recordsLinked to original sources
arXiv2025

Spectral Methods in Microeconomics

Matrices often appear in formal models of social and economic behavior, especially models involving networks. Such models are used to study subjects ranging from opinion dynamics to pollution-mitigation negotiations to the regulation of large marketplace platforms. Matrices are used to capture the focal economic structure in each case. Spectral theory offers powerful tools for understanding matrices, and economic modelers have leveraged these tools to gain considerable insight. When special structure is present, such as nonnegativity or symmetry, more refined tools suited to this structure -- such as Perron--Frobenius theory and the spectral theorem -- offer additional leverage. This essay uses these unifying mathematical threads to offer an accessible tour of several important ideas in social science, assuming minimal non-mathematical background knowledge. Though the introductions to each topic are necessarily brief, the tour cites references throughout for more context.

econ.TH↗
arXiv2024

Multiplexing in Networks and Diffusion

Social and economic networks are often multiplexed, meaning that people are connected by different types of relationships -- such as borrowing goods and giving advice. We make two contributions to the study of multiplexing and the understanding of simple versus complex contagion. On the theoretical side, we introduce a model and theoretical results about diffusion in multiplex networks. We show that multiplexing impedes the spread of simple contagions, such as diseases or basic information that only require one interaction to transmit an infection. We show, however that multiplexing enhances the spread of a complex contagion when infection rates are low, but then impedes complex contagion if infection rates become high. On the empirical side, we document empirical multiplexing patterns in Indian village data. We show that relationships such as socializing, advising, helping, and lending are correlated but distinct, while commonly used proxies for networks based on ethnicity and geography are nearly uncorrelated with actual relationships. We also show that these layers and their overlap affect information diffusion in a field experiment. The advice network is the best predictor of diffusion, but combining layers improves predictions further. Villages with greater overlap between layers -- more multiplexing -- experience less overall diffusion. Finally, we identify differences in multiplexing by gender and connectedness. These have implications for inequality in diffusion-mediated outcomes such as access to information and adherence to norms.

econ.GN↗
arXiv2024

Incentive Design with Spillovers

A principal uses payments conditioned on stochastic outcomes of a team project to elicit costly effort from the team members. We develop a multi-agent generalization of a classic first-order approach to contract optimization by leveraging methods from network games. The main results characterize the optimal allocation of incentive pay across agents and outcomes. Incentive optimality requires equalizing, across agents, a product of (i) individual productivity (ii) organizational centrality and (iii) responsiveness to monetary incentives. We specialize the model to explore several applied questions, including whether compensation should reward individual ability or collaborativeness and how the strength of complementarities shapes pay dispersion.

econ.TH↗
arXiv2024

Robust Market Interventions

When can interventions in markets be designed to increase surplus robustly -- i.e., with high probability -- accounting for uncertainty due to imprecise information about economic primitives? In a setting with many strategic firms, each possessing some market power, we present conditions for such interventions to exist. The key condition, recoverable structure, requires large-scale complementarities among families of products. The analysis works by decomposing the incidence of interventions in terms of principal components of a Slutsky matrix. Under recoverable structure, a noisy signal of this matrix reveals enough about these principal components to design robust interventions. Our results demonstrate the usefulness of spectral methods for analyzing imperfectly observed strategic interactions with many agents.

econ.TH↗
arXiv2024

Games on Endogenous Networks

We study network games in which players choose both the partners with whom they associate and an action level (e.g., effort) that creates spillovers for those partners. We introduce a framework and two solution concepts, extending standard approaches for analyzing each choice in isolation: Nash equilibrium in actions and pairwise stability in links. Our main results show that, under suitable order conditions on incentives, stable networks take simple forms. The first condition concerns whether links create positive or negative payoff spillovers. The second concerns whether actions are strategic complements to links, or strategic substitutes. Together, these conditions yield a taxonomy of the relationship between network structure and economic primitives organized around two network architectures: ordered overlapping cliques and nested split graphs. We apply our model to understand the consequences of competition for status, to microfound matching models that assume clique formation, and to interpret empirical findings that highlight unintended consequences of group design.

econ.TH↗
arXiv2023

Equity Pay In Networked Teams

A group of agents each exert effort to produce a joint output, with the complementarities between their efforts represented by a (weighted) network. Under equity compensation, a principal motivates the agents to work by giving them shares of the output. We describe the optimal equity allocation. It is characterized by a neighborhood balance condition: any two agents receiving equity have the same (weighted) total equity assigned to their neighbors. We also study the problem of selecting the team of agents who receive positive equity, and show this team must form a tight-knit subset of the complementarity network, with any pair being complementary to one another or jointly to another team member. Finally, we give conditions under which the amount of equity used for compensation is increasing in the strength of a team's complementarities and discuss several other applications.

econ.TH↗
arXiv2023

Supply Network Formation and Fragility

We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships stronger, trading off the cost of investment against the benefits of increased robustness. A supply network is called fragile if aggregate output is very sensitive to small aggregate shocks. We show that supply networks of intermediate productivity are fragile in equilibrium, even though this is always inefficient. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks.

econ.TH↗
arXiv2023

On the Difficulty of Characterizing Network Formation with Endogenous Behavior

Bolletta (2021, Math. Soc. Sci. 114:1-10) studies a model in which a network is strategically formed and then agents play a linear best-response investment game in it. The model is motivated by an application in which people choose both their study partners and their levels of educational effort. Agents have different one-dimensional types $\unicode{x2013}$ private returns to effort. A main result claims that pairwise Nash stable networks have a locally complete structure consisting of possibly overlapping cliques: if two agents are linked, they are part of a clique composed of all agents with types between theirs. We offer a counterexample showing that the claimed characterization is incorrect, highlight where the analysis errs, and discuss implications for network formation models.

econ.TH↗
arXiv2023

Corporate Culture and Organizational Fragility

Complex organizations accomplish tasks through many steps of collaboration among workers. Corporate culture supports collaborations by establishing norms and reducing misunderstandings. Because a strong corporate culture relies on costly, voluntary investments by many workers, we model it as an organizational public good, subject to standard free-riding problems, which become severe in large organizations. Our main finding is that voluntary contributions to culture can nevertheless be sustained, because an organization's equilibrium productivity is endogenously highly sensitive to individual contributions. However, the completion of complex tasks is then necessarily fragile to small shocks that damage the organization's culture.

econ.TH↗
arXiv2022

Learning from Neighbors about a Changing State

Agents learn about a changing state using private signals and their neighbors' past estimates of the state. We present a model in which Bayesian agents in equilibrium use neighbors' estimates simply by taking weighted sums with time-invariant weights. The dynamics thus parallel those of the tractable DeGroot model of learning in networks, but arise as an equilibrium outcome rather than a behavioral assumption. We examine whether information aggregation is nearly optimal as neighborhoods grow large. A key condition for this is signal diversity: each individual's neighbors have private signals that not only contain independent information, but also have sufficiently different distributions. Without signal diversity $\unicode{x2013}$ e.g., if private signals are i.i.d. $\unicode{x2013}$ learning is suboptimal in all networks and highly inefficient in some. Turning to social influence, we find it is much more sensitive to one's signal quality than to one's number of neighbors, in contrast to standard models with exogenous updating rules.

econ.TH↗
arXiv2022

Taxes and Market Power: A Principal Components Approach

Suppliers of differentiated goods make simultaneous pricing decisions, which are strategically linked. Because of market power, the equilibrium is inefficient. We study how a policymaker should target a budget-balanced tax-and-subsidy policy to increase welfare. A key tool is a certain basis for the goods space, determined by the network of interactions among suppliers. It consists of eigenbundles -- orthogonal in the sense that a tax on any eigenbundle passes through only to its own price -- with pass-through coefficients determined by associated eigenvalues. Our basis permits a simple characterization of optimal interventions. A planner maximizing consumer surplus should tax eigenbundles with low pass-through and subsidize ones with high pass-through. The Pigouvian leverage of the system -- the gain in consumer surplus achievable by an optimal tax scheme -- depends only on the dispersion of the eigenvalues of the matrix of strategic interactions. We interpret these results in terms of the network structure of the market.

econ.TH↗
arXiv2021

A Network Approach to Public Goods: A Short Summary

Suppose agents can exert costly effort that creates nonrival, heterogeneous benefits for each other. At each possible outcome, a weighted, directed network describing marginal externalities is defined. We show that Pareto efficient outcomes are those at which the largest eigenvalue of the network is 1. An important set of efficient solutions, Lindahl outcomes, are characterized by contributions being proportional to agents' eigenvector centralities in the network. The outcomes we focus on are motivated by negotiations. We apply the results to identify who is essential for Pareto improvements, how to efficiently subdivide negotiations, and whom to optimally add to a team.

econ.TH↗
arXiv2021

Discord and Harmony in Networks

Consider a coordination game played on a network, where agents prefer taking actions closer to those of their neighbors and to their own ideal points in action space. We explore how the welfare outcomes of a coordination game depend on network structure and the distribution of ideal points throughout the network. To this end, we imagine a benevolent or adversarial planner who intervenes, at a cost, to change ideal points in order to maximize or minimize utilitarian welfare subject to a constraint. A complete characterization of optimal interventions is obtained by decomposing interventions into principal components of the network's adjacency matrix. Welfare is most sensitive to interventions proportional to the last principal component, which focus on local disagreement. A welfare-maximizing planner optimally works to reduce local disagreement, bringing the ideal points of neighbors closer together, whereas a malevolent adversary optimally drives neighbors' ideal points apart to decrease welfare. Such welfare-maximizing/minimizing interventions are very different from ones that would be done to change some traditional measures of discord, such as the cross-sectional variation of equilibrium actions. In fact, an adversary sowing disagreement to maximize her impact on welfare will minimize her impact on global variation in equilibrium actions, underscoring a tension between improving welfare and increasing global cohesion of equilibrium behavior.

econ.TH↗
arXiv2020

Expectations, Networks, and Conventions

In coordination games and speculative over-the-counter financial markets, solutions depend on higher-order average expectations: agents' expectations about what counterparties, on average, expect their counterparties to think, etc. We offer a unified analysis of these objects and their limits, for general information structures, priors, and networks of counterparty relationships. Our key device is an interaction structure combining the network and agents' beliefs, which we analyze using Markov methods. This device allows us to nest classical beauty contests and network games within one model and unify their results. Two applications illustrate the techniques: The first characterizes when slight optimism about counterparties' average expectations leads to contagion of optimism and extreme asset prices. The second describes the tyranny of the least-informed: agents coordinating on the prior expectations of the one with the worst private information, despite all having nearly common certainty, based on precise private signals, of the ex post optimal action.

econ.TH↗
arXiv2020

Notes on a Social Transmission Model with a Continuum of Agents

This note presents a simple overlapping-generations (OLG) model of the transmission of a trait, such as a culture. Initially, some fraction of agents carry the trait. In each time period, young agents are "born" and are influenced by some older agents. Agents adopt the trait only if at least a certain number of their influencers have the trait. This influence may occur due to rational choice (e.g., because the young agents are playing a coordination game with old agents who are already committed to a strategy), or for some other reason. Our interest is in how the process of social influence unfolds over time, and whether a trait will persist or die out. We characterize the dynamics of the fraction of active agents and relate the analysis to classic results on branching processes and random graphs.

physics.soc-ph↗
arXiv2020

Targeting Interventions in Networks

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 involve a single principal component.

cs.GT↗
arXiv2017

Revisiting Imidazolium Based Ionic Liquids: Effect of the Conformation Bias of the [NTf$_{2}$] Anion Studied By Molecular Dynamics Simulations

We study ionic liquids composed 1-alkyl-3-methylimidazolium cations and bis(trifluoromethyl-sulfonyl)imide anions ([C$_n$MIm][NTf$_2$]) with varying chain-length $n\!=\!2, 4, 6, 8$ by using molecular dynamics simulations. We show that a reparametrization of the dihedral potentials as well as charges of the [NTf$_2$] anion leads to an improvment of the force field model introduced by Köddermann {\em et al.} [ChemPhysChem, \textbf{8}, 2464 (2007)] (KPL-force field). A crucial advantage of the new parameter set is that the minimum energy conformations of the anion ({\em trans} and {\em gauche}), as deduced from {\em ab initio} calculations and {\sc Raman} experiments, are now both well represented by our model. In addition, the results for [C$_n$MIm][NTf$_2$] show that this modification leads to an even better agreement between experiment and molecular dynamics simulation as demonstrated for densities, diffusion coefficients, vaporization enthalpies, reorientational correlation times, and viscosities. Even though we focused on a better representation of the anion conformation, also the alkyl chain-length dependence of the cation behaves closer to the experiment. We strongly encourage to use the new NGKPL force field for the [NTf$_2$] anion instead of the earlier KPL parameter set for computer simulations aiming to describe the thermodynamics, dynamics and also structure of imidazolium based ionic liquids.

cond-mat.soft↗