The cost of segregation in (social) networks

This paper investigates the welfare effect of income redistribution in the private provision of public goods on networks. We first show that the welfare effect of income redistribution is determined by Bonacich centrality. Then we develop an index based on the network structure of interactions, which, roughly speaking, measures the welfare effect of income redistribution confined to a component of contributors. The proposed index vanishes when applied to large components of contributors that display special segregated interactions, which suggests an “asymptotic neutrality” of redistributive policies. JEL classification C72; D31; H4

Testing Core Membership in Public Goods Economies

This paper develops a recent line of economic theory seeking to understand public goods economies using methods of topological analysis. Our first main result is a very clean characterization of the economy's core (the standard solution concept in public goods). Specifically, we prove that a point is in the core iff it is Pareto efficient, individually rational, and the set of points it dominates is path connected. While this structural theorem has a few interesting implications in economic theory, the main focus of the second part of this paper is on a particular algorithmic application that demonstrates its utility. Since the 1960s, economists have looked for an efficient computational process that decides whether or not a given point is in the core. All known algorithms so far run in exponential time (except in some artificially restricted settings). By heavily exploiting our new structure, we propose a new algorithm for testing core membership whose computational bottleneck is the solution of $O(n)$ convex optimization problems on the utility function governing the economy. It is fairly natural to assume that convex optimization should be feasible, as it is needed even for very basic economic computational tasks such as testing Pareto efficiency. Nevertheless, even without this assumption, our work implies for the first time that core membership can be efficiently tested on (e.g.) utility functions that admit "nice" analytic expressions, or that appropriately defined $\varepsilon$-approximate versions of the problem are tractable (by using modern black-box $\varepsilon$-approximate convex optimization algorithms).Comment: To appear in ICALP 201

Testing Core Membership in Public Goods Economies

This paper develops a recent line of economic theory seeking to understand public goods economies using methods of topological analysis. Our first main result is a very clean characterization of the economy\u27s core (the standard solution concept in public goods). Specifically, we prove that a point is in the core iff it is Pareto efficient, individually rational, and the set of points it dominates is path connected. While this structural theorem has a few interesting implications in economic theory, the main focus of the second part of this paper is on a particular algorithmic application that demonstrates its utility. Since the 1960s, economists have looked for an efficient computational process that decides whether or not a given point is in the core. All known algorithms so far run in exponential time (except in some artificially restricted settings). By heavily exploiting our new structure, we propose a new algorithm for testing core membership whose computational bottleneck is the solution of O(n) convex optimization problems on the utility function governing the economy. It is fairly natural to assume that convex optimization should be feasible, as it is needed even for very basic economic computational tasks such as testing Pareto efficiency. Nevertheless, even without this assumption, our work implies for the first time that core membership can be efficiently tested on (e.g.) utility functions that admit ``nice\u27\u27 analytic expressions, or that appropriately defined epsilon-approximate versions of the problem are tractable (by using modern black-box epsilon-approximate convex optimization algorithms)

Some new aspects of main eigenvalues of graphs

An eigenvalue of the adjacency matrix of a graph is said to be main if the all-1 vector is non-orthogonal to the associated eigenspace. This paper explores some new aspects of the study of main eigenvalues of graphs, investigating specifically cones over strongly regular graphs and graphs for which the least eigenvalue is non-main. In this case, we characterize paths and trees with diameter-3 satisfying the property. We may note that the importance of least eigenvalues of graphs for the equilibria of social and economic networks was recently uncovered in literature.publishe

Constrained public goods in networks

This paper analyses the private provision of public goods where agents interact within a fixed network structure and may benefit only from their direct neighbours’ provisions. We generalise the public goods in networks model of Bramoullé and Kranton (2007) to allow for constrained provision. In so doing, we characterise Nash equilibria with no intermediate contributors

A network approach to public goods

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

Dirty neighbors — Pollution in an interlinked world

We apply a network approach to analyze individual and aggregate consumption that generates predominately local pollution (e.g., noise, water and air quality, waste disposal sites). This allows us to relate the individual pollution levels to network centralities and to determine the effects of transfers among agents on the aggregate contamination. We then apply our theoretical framework to analyze the European data on fossil fuel energy consumption and discuss the impact of EU redistributive transfer policies on the aggregate level of pollution

The Cost of Sharing Information in a Social World

With the increasing prevalence of large scale online social networks, the field has evolved from studying small scale networks and interactions to massive ones that encompass huge fractions of the world’s population. While many methods focus on techniques at scale applied to a single domain, methods that apply techniques across multiple domains are becoming increasingly important. These methods rely on understanding the complex relationships in the data. In the context of social networks, the big data available allows us to better model and analyze the flow of information within the network. The first part of this thesis discusses methods to more effectively learn and predict in a social network by leveraging information across multiple domains and types of data. We document a method to identify users from their access to content in a network and their click behavior. Even on a macro level, click behavior is often hard to obtain. We describe a technique to predict click behavior using other public information about the social network. Communication within a network inevitably has some bias that can be attributed to individual preferences and quality as well as the underlying structure of the network. The second part of the thesis characterizes the structural bias in a network by modeling the underlying information flow as a commodity of trade

Essays in Microeconomic Theory

We present a collection of three essays exploring topics in microeconomic theory: conflict, alliances, and the origins of society; supply chain networks and industrial organisation; and game theory on economic networks. Chapter 1 Anthropological evidence has shown that humans in the earliest agricultural societies worked harder and had lesser health outcomes than humans in hunter-gatherer societies. We develop a model where hunting and gathering is more productive than agriculture, yet individually rational actors coordinate on a less productive agricultural equilibrium. In an agricultural society, a group of warriors with dominant fighting skills threaten hunters into subjugation and tax farmers a portion of their produce. We develop three submodels: a simple model where all agents are worse off than in a hunter-gatherer society, a model with inequality where warriors improve their payoff relative to hunting and gathering at the expense of all other agents, and a dynamic model describing the transition from a hunter-gatherer society to an agricultural society. Chapter 2 Barriers to trade can create price discrepancies between markets. We apply this concept to an intermediation network, where the price at each node varies inversely with the quantity of resource supplied. We model a directed multipartite graph of intermediaries between a source and a market, where intermediaries in each partition simultaneously compete in the manner of Cournot competition, selecting the quantity of resource sold along each of their out-links. The linking structure represents each intermediary's opportunity to sell the resource. We derive an analytical solution determining the quantity decisions of each intermediary in the network, which we believe is the first such solution for a Cournot-driven supply chain. We discuss the efficiency of networks, and develop a measure that evaluates networks according to the consumer surplus received at the market. Chapter 3 A set of agents is connected by two distinct networks, with each network describing access to a different local public good. Agents choose in which networks to invest, and neighbouring agents' investments in the same good are strategic substitutes, as are an agent's two investment choices. There are always equilibria where any investing agent bears all local investment costs and others free-ride. When investment in one good reduces marginal benefit from investment in the other, agents free-riding in one good may invest more profitably in the other, and equilibrium payoffs are more evenly distributed. This need not reduce aggregate payoff