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We develop a tractable model of endogenous production networks. Each one of a number of products can be produced by combining labor and an endogenous subset of the other products as inputs. Different combinations of inputs generate (prespecified) levels of productivity and various distortions may affect costs and prices. We establish the existence and uniqueness of an equilibrium and provide comparative static results on how prices and endogenous technology/input choices (and thus the production network) respond to changes in parameters. These results show that improvements in technology (or reductions in distortions) spread throughout the economy via input–output linkages and reduce all prices, and under reasonable restrictions on the menu of production technologies, also lead to a denser production network. Using a dynamic version of the model, we establish that the endogenous evolution of the production network could be a powerful force towards sustained economic growth. At the root of this result is the fact that the arrival of a few new products expands the set of technological possibilities of all existing industries by a large amount—that is, if there are n products, the arrival of one more new product increases the combinations of inputs that each existing product can use from 2n-1 to 2ⁿ, thus enabling significantly more pronounced cost reductions from choice of input combinations. These cost reductions then spread to other industries via lower input prices and incentivize them to also adopt additional inputs.

I introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent-level heterogeneity in link surplus (degree heterogeneity). Like in fixed effects panel data analyses, the joint distribution of observed and unobserved agent-level characteristics is left unrestricted. Two estimators for the (common) homophily parameter, β₀, are developed and their properties studied under an asymptotic sequence involving a single network growing large. The first, tetrad logit (TL), estimator conditions on a sufficient statistic for the degree heterogeneity. The second, joint maximum likelihood (JML), estimator treats the degree heterogeneity $\\left\\{ {{A_{i0}}} \\right\\}_{i = 1}^N$ as additional (incidental) parameters to be estimated. The TL estimate is consistent under both sparse and dense graph sequences, whereas consistency of the JML estimate is shown only under dense graph sequences.

This paper provides a framework for identifying preferences in a large network where links are pairwise stable. Network formation models present difficulties for identification, especially when links can be interdependent, for example, when indirect connections matter. We show how one can use the observed proportions of various local network structures to learn about the underlying preference parameters. The key assumption for our approach restricts individuals to have bounded degree in equilibrium, implying a finite number of payoff-relevant local structures. Our main result provides necessary conditions for parameters to belong to the identified set. We then develop a quadratic programming algorithm that can be used to construct this set. With further restrictions on preferences, we show that our conditions are also sufficient for pairwise stability and therefore characterize the identified set precisely. Overall, the use of both the economic model along with pairwise stability allows us to obtain effective dimension reduction.

There is a large and growing literature on peer effects in economics. In the current article, we focus on a Manski-type linear-in-means model that has proved to be popular in empirical work. We critically examine some aspects of the statistical model that may be restrictive in empirical analyses. Specifically, we focus on three aspects. First, we examine the endogeneity of the network or peer groups. Second, we investigate simultaneously alternative definitions of links and the possibility of peer effects arising through multiple networks. Third, we highlight the representation of the traditional linear-in-means model as an autoregressive model, and contrast it with an alternative moving-average model, where the correlation between unconnected individuals who are indirectly connected is limited. Using data on friendship networks from the Add Health dataset, we illustrate the empirical relevance of these ideas.

Social and economic networks are ubiquitous, serving as contexts for job search, technology diffusion, the accumulation of human capital, and even the formulation of norms and values. The systematic empirical study of network formation—the process by which agents form, maintain, and dissolve links—within economics is recent, is associated with extraordinarily challenging modeling and identification issues, and is an area of exciting new developments, with many open questions. This article reviews prominent research on the empirical analysis of network formation, with an emphasis on contributions made by economists.

The objective of this paper is to identify and estimate network formation models using observed data on network structure. We characterize network formation as a simultaneous-move game, where the utility from forming a link depends on the structure of the network, thereby generating strategic interactions between links. With the prevalence of multiple equilibria, the parameters are not necessarily point identified. We leave the equilibrium selection unrestricted and propose a partial identification approach. We derive bounds on the probability of observing a subnetwork, where a subnetwork is the restriction of a network to a subset of the individuals. Unlike the standard bounds as in Ciliberto and Tamer (2009), these subnetwork bounds are computationally tractable in large networks provided we consider small subnetworks. We provide Monte Carlo evidence that bounds from small subnetworks are informative in large networks.

Biopolymer networks contribute mechanical integrity as well as functional organization to living cells. One of their major constituents, the protein actin, is present in a large variety of different network architectures, ranging from extensive networks to densely packed bundles. The shape of the network is directly linked to its mechanical properties and essential physiological functions. However, a profound understanding of architecture-determining mechanisms and their physical constraints remains elusive. We use experimental bottom-up systems to study the formation of confined actin networks by entropic forces. Experiments based on molecular crowding as well as counterion condensation reveal a generic tendency of homogeneous filament solutions to aggregate into regular actin bundle networks connected by aster-like centers. The network architecture is found to critically rely on network formation history. Starting from identical biochemical compositions, we observe drastic changes in network architecture as a consequence of initially biased filament orientation or mixing-induced perturbations. Our experiments suggest that the tendency to form regularly spaced bundle networks is a rather general feature of isotropic, homogeneous filament solutions subject to uniform attractive interactions. Due to the fundamental nature of the considered interactions, we expect that the investigated type of network formation further implies severe physical constraints for cytoskeleton self-organization on the more complex level of living cells.

We develop a dynamic network formation model that can explain the observed nestedness in real-world networks. Links are formed on the basis of agents' centrality and have an exponentially distributed life time. We use stochastic stability to identify the networks to which the network formation process converges and find that they are nested split graphs. We completely determine the topological properties of the stochastically stable networks and show that they match features exhibited by real-world networks. Using four different network datasets, we empirically test our model and show that it fits well the observed networks.

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.

We study the effect of a common enemy on the connections-model of network formation, where self-interested players can use links to build a network, knowing that they face a common enemy who can disrupt the links or nodes of the network. The goal of the common enemy is to minimize the sum of the benefits players obtain from the network. We find that for large linking costs, introducing such a common enemy can lead to the formation of pairwise stable and efficient networks which would not be pairwise stable without the threat of disruption. The reason is the large reduction in payoffs caused by disruption as soon as one player fails to maintain a link. However, we also find that for small linking costs, the empty network is pairwise stable under disruption, whereas it is not in the absence of disruption. The reason is that in the presence of disruption a link that is unilaterally formed is automatically targeted (or one of the players forming the link is automatically targeted). While the common enemy can thus have a positive effect on the incentives of the players to form an efficient network, it can also lead to the disintegration of the network.