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154
Social Capital
 In P. Aghion, S.N. Durlauf, eds, Handbook of Economic Growth
, 2006
"... have provided excellent research assistance. I thank Stephen Machin and three referees for ..."
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Cited by 71 (5 self)
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have provided excellent research assistance. I thank Stephen Machin and three referees for
Complex Networks and Decentralized Search Algorithms
 In Proceedings of the International Congress of Mathematicians (ICM
, 2006
"... The study of complex networks has emerged over the past several years as a theme spanning many disciplines, ranging from mathematics and computer science to the social and biological sciences. A significant amount of recent work in this area has focused on the development of random graph models that ..."
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Cited by 71 (1 self)
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The study of complex networks has emerged over the past several years as a theme spanning many disciplines, ranging from mathematics and computer science to the social and biological sciences. A significant amount of recent work in this area has focused on the development of random graph models that capture some of the qualitative properties observed in largescale network data; such models have the potential to help us reason, at a general level, about the ways in which realworld networks are organized. We survey one particular line of network research, concerned with smallworld phenomena and decentralized search algorithms, that illustrates this style of analysis. We begin by describing a wellknown experiment that provided the first empirical basis for the "six degrees of separation" phenomenon in social networks; we then discuss some probabilistic network models motivated by this work, illustrating how these models lead to novel algorithmic and graphtheoretic questions, and how they are supported by recent empirical studies of large social networks.
The Price of Selfish Behavior in Bilateral Network Formation
, 2005
"... Given a collection of selfish agents who wish to establish links to route traffic among themselves, the set of equilibrium network topologies may appear quite different from the centrally enforced optimum. We study the quality (price of anarchy) of equilibrium networks in a game where links require ..."
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Cited by 61 (0 self)
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Given a collection of selfish agents who wish to establish links to route traffic among themselves, the set of equilibrium network topologies may appear quite different from the centrally enforced optimum. We study the quality (price of anarchy) of equilibrium networks in a game where links require the consent of both participants and are negotiated bilaterally and compare these networks to those generated by an earlier model due to Fabrikant et al. [6] in which links are formed unilaterally. We provide a characterization of stable and efficient networks in the bilateral network formation game, show that the set of stable networks is richer than those in the unilateral game, and that all stable networks of the unilateral game are also stable in the bilateral game. We also provide an upper and lower bound on the price of anarchy (tight in the size of the network n but not the link cost α) of the bilateral game and show that the worstcase price of anarchy of the bilateral model is worse than for the unilateral model. A careful empirical analysis demonstrates that the average price of anarchy is better in the bilateral connection game than in the unilateral game for small link costs but worse as links become more expensive. In the process, a powerful equivalence between linkbased graph stability and two gametheoretic equilibrium notions is also discussed. The equivalence establishes necessary and sufficient conditions for an equilibrium in the bilateral game that helps provide a partial geometric characterization of equilibrium graphs.
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
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Cited by 53 (0 self)
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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
The economics of social networks
 PROCEEDINGS OF THE 9 TH WORLD CONGRESS OF THE ECONOMETRIC SOCIETY
, 2005
"... The science of social networks is a central field of sociological study, a major application of random graph theory, and an emerging area of study by economists, statistical physicists and computer scientists. While these literatures are (slowly) becoming aware of each other, and on occasion drawing ..."
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Cited by 53 (2 self)
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The science of social networks is a central field of sociological study, a major application of random graph theory, and an emerging area of study by economists, statistical physicists and computer scientists. While these literatures are (slowly) becoming aware of each other, and on occasion drawing from one another, they are still largely distinct in their methods, interests, and goals. Here, my aim is to provide some perspective on the research from these literatures, with a focus on the formal modeling of social networks and the two major types of models: those based on random graphs and those based on game theoretic reasoning. I highlight some of the strengths, weaknesses, and potential synergies between these two network modeling approaches.
Network Design with Weighted Players
 In Proceedings of the 18th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2006
"... We consider a model of gametheoretic network design initially studied by Anshelevich et al. [2], where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its p ..."
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Cited by 44 (6 self)
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We consider a model of gametheoretic network design initially studied by Anshelevich et al. [2], where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its path is the fixed cost of the edge divided by the number of players using it. In this special case, Anshelevich et al. [2] proved that purestrategy Nash equilibria always exist and that the price of stability—the ratio in costs of a minimumcost Nash equilibrium and an optimal solution—is Θ(log k), where k is the number of players. Little was known about the existence of equilibria or the price of stability in the general weighted version of the game. Here, each player i has aweightwi≥1, and its cost share of an edge in its path
The effects of social networks on employment and inequality
 American Economic Review
, 2004
"... We develop a model where agents obtain information about job opportunities through an explicitly modeled network of social contacts. We show that employment is positively correlated across time and agents. Moreover, unemployment exhibits duration dependence: the probability of obtaining a job decrea ..."
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Cited by 38 (1 self)
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We develop a model where agents obtain information about job opportunities through an explicitly modeled network of social contacts. We show that employment is positively correlated across time and agents. Moreover, unemployment exhibits duration dependence: the probability of obtaining a job decreases in the length of time that an agent has been unemployed. Finally, we examine inequality between two groups. If staying in the labor market is costly and one group starts with a worse employment status, then that group’s dropout rate will be higher and their employment prospects will be persistently below that of the other group. (JEL A14, J64, J31, J70) The importance of social networks in labor markets is pervasive and well documented. Mark Granovetter (1973, 1995) found in a survey of residents of a Massachusetts town that over 50 percent of jobs were obtained through social contacts. Earlier work by Albert Rees (1966) found numbers of over 60 percent in a similar study. Exploration in a large number of studies documents similar figures for a variety of occupations, skill levels, and socioeconomic backgrounds. 1 In this paper, we take the role of social networks as a manner of obtaining information about job opportunities as a given and explore its implications for the dynamics of employment. In particular, we examine a simple model of the transmission of job information through a network of social contacts. Each agent is connected to others through a network. Information
Neighborhood Effects
 PREPARED FOR THE HANDBOOK OF REGIONAL AND URBAN ECONOMICS, VOLUME 4,
, 2003
"... This paper surveys the modern economics literature on the role of neighborhoods in influencing socioeconomic outcomes. Neighborhood effects have been analyzed in a range of theoretical and applied contexts and have proven to be of interest in understanding questions ranging from the asymptotic prope ..."
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Cited by 37 (0 self)
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This paper surveys the modern economics literature on the role of neighborhoods in influencing socioeconomic outcomes. Neighborhood effects have been analyzed in a range of theoretical and applied contexts and have proven to be of interest in understanding questions ranging from the asymptotic properties of various evolutionary games to explaining the persistence of poverty in inner cities. As such, the survey covers a range of theoretical, econometric and empirical topics. One conclusion from the survey is that there is a need to better integrate findings from theory and econometrics into empirical studies; until this is done, empirical studies of the nature and magnitude of neighborhood effects are unlikely to persuade those skeptical about their importance.
The Formation of Networks with Transfers among Players
 J. ECONOMIC THEORY
, 2004
"... We examine the formation of networks among a set of players whose payoffs depend on the structure of the network. We focus on games where players may bargain by promising or demanding transfer payments when forming links. We examine several variations of the transfer/bargaining aspect of link for ..."
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Cited by 32 (5 self)
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We examine the formation of networks among a set of players whose payoffs depend on the structure of the network. We focus on games where players may bargain by promising or demanding transfer payments when forming links. We examine several variations of the transfer/bargaining aspect of link formation. One aspect is whether players can only make and receive transfers to other players to whom they are directly linked, or whether they can also subsidize links that they are not directly involved in. Another aspect is whether or not transfers related to a given link can be made contingent on the full resulting network or only on the link itself. A final aspect is whether or not players can pay other players to refrain from forming links. We characterize the networks that are supported under these variations and show how each of the above aspects is related either to accounting for a specific type of externality, or to dealing with the combinatorial nature of network payoffs.
Designing networks with good equilibria
 In SODA ’08
, 2007
"... In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network co ..."
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Cited by 30 (4 self)
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In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge costsharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal costsharing protocols for undirected and directed graphs, singlesink and multicommodity networks, different classes of costsharing methods, and different measures of the inefficiency of equilibria. One of our main technical tools is a complete characterization of the uniform costsharing protocols—protocols that are designed without foreknowledge of or assumptions on the network in which they will be deployed. We use this characterization result to identify the optimal uniform protocol in several scenarios: for example, the Shapley protocol is optimal in directed graphs, while the optimal protocol in undirected graphs, a simple priority scheme, has exponentially smaller worstcase price of anarchy than the Shapley protocol. We also provide several matching upper and lower bounds on the bestpossible performance of nonuniform costsharing protocols.