15 research outputs found

    The cost of segregation in (social) networks

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    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

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    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)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 ε\varepsilon-approximate versions of the problem are tractable (by using modern black-box ε\varepsilon-approximate convex optimization algorithms).Comment: To appear in ICALP 201

    Testing Core Membership in Public Goods Economies

    Get PDF
    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

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    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

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    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

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    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

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    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
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