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Sanjeev Goyal

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"The economy . . . will be one of the greatest beneficiaries of network thinking. Goyal's Connections, the first comprehensive treatment of network economics, is an important step in this fascinating journey."--Albert-Laszlo Barabasi, Department of Physics, Northeastern University

"This book provides a comprehensive account of the antecedents and consequences of networks. Scholars who are interested in a boundary-spanning account of this important phenomenon will find this book to be extremely valuable."--Ranjay Gulati, Harvard Business School

"Networks is becoming a new and exciting interdisciplinary research area integrating ideas from many fields, including sociology, economics, and computer science, in each case studying how networks and the social setting affect outcomes. Connections provides an excellent introduction to this emerging area from an economic perspective, and will be invaluable for researchers interested in any aspect of the subject."--Eva Tardos, Department of Computer Science, Cornell University

"Sanjeev Goyal presents a clear and comprehensive account of the work in this field to which he is a major contributor. Connections analyzes two important questions. How does the structure of the network of interactions influence economic outcomes and how do networks evolve if people can consciously choose those with whom they want to be linked?"--Alan Kirman, L'école des Hautes études en Sciences Sociales, Université D'Aix Marseille III, Institut Universitaire de France

"This book is an excellent introduction to the theory of social networks and should be the top choice for any graduate student interested in the subject."--Markus Mobius, Department of Economics, Harvard University

"Connections provides an overview of the new and exciting economic approach to social networks. Accessible to noneconomists and providing a wide range of illustrations, including information-sharing networks, research-collaboration networks among firms, and labor-market networks, the book addresses two main questions: How does a pattern of connections influence behaviors, the efficiency of outcomes, and the diffusion of information? And what are the incentives to establish connections in the first place? Highly recommended."--Gabrielle Demange, L'Ecole des Hautes Etudes en Sciences Sociales, Paris

"Written by a pioneer and leading contributor in the field, Connections provides an authoritative account of the recent economic literature on networks. It discusses theoretical models, economic applications, and empirical evidence on networks in a clear, concise, and vivid fashion. Undoubtedly, this book will prove to be invaluable, both as a reference on network theory and as a textbook for advanced students in economic theory."--Francis Bloch, GREQAM, Marseille; and University of Warwick

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Connections

Princeton University Press

Contents

Acknowledgements............................................ix1 Introduction..............................................12 Networks: Concepts and Empirics...........................93 Games on Networks.........................................254 Coordination and Cooperation..............................635 Social Learning...........................................876 Social Networks in Labor Markets..........................1137 Strategic Network Formation: Concepts.....................1438 One-Sided Link Formation..................................1639 Two-Sided Link Formation..................................19910 Research Collaboration among Firms.......................245References..................................................271Index.......................................................285

Chapter One

1.1 Themes

I buy a new computer every few years. A computer is a sophisticated product and there are a number of different options open to me. To make an informed choice, I personally gather information on the different brands and models available—by going on the World Wide Web, visiting computer shops, and reading computer magazines—and I talk to my colleagues and friends to get tips about the different brands available. The time and effort I personally spend in collecting information depend very much on how well-informed my friends and colleagues are: if they are well-informed, then I rely upon their information and do not spend much time in collecting information myself.

My friends and colleagues face a similar situation, and their own efforts at collecting information in turn depend on how much information their acquaintances (including me) collect personally. Thus my efforts at collecting information personally will depend on the efforts of those whom I know, and the efforts of these individuals will in turn depend on the efforts of their friends, and so on. This suggests that individual choices concerning the gathering of information are shaped by the pattern of connections between persons in a society.

Indeed, it may well be worth my while to form connections with someone who is well-informed rather than carrying out the search myself. Moreover, I should compare the costs in terms of time and effort involved in forming such a connection with the potential benefits of obtaining valuable information. This line of reasoning leads us to the idea that the pattern of connections that obtain in a society will themselves reflect rational decision making of individuals.

This story helps us in framing two primary questions:

(i) What are the economic effects of the pattern of connections that obtain in a society?

(ii) What is the architecture of connections that emerges when individual entities form links with each other based on considerations of personal costs and benefits?

The study of these questions constitutes the subject matter of this book.

Relationships among individuals have a number of different dimensions. The first task is therefore to find a conceptual framework within which they can be described and then measured in a meaningful manner. We also need a language within which variations in relationships can be naturally expressed. The concept of a network addresses these requirements nicely: a network describes a collection of nodes and the links between them. The notion of nodes is fairly general: they may be individuals or firms or countries, or even collections of such entities. A link between two nodes signifies a direct relation between them; for instance, in a social context a link could be a friendship tie, while in the context of countries a link may be a free trade agreement or a mutual defense pact. Networks have been studied extensively in mathematics in the theory of graphs, and they have also been applied in a number of different subjects such as sociology, computer science, and statistical physics. Chapter 2 draws on these literatures to present the principal network concepts and notation which are used throughout the book. This chapter also identifies a number of common features in empirical networks. This discussion directs our attention to specific networks in our theoretical investigations of the subsequent chapters.

The first substantive part of the book, comprising chapters 3–6, studies the effects of network structures on individual behavior. Chapters 3 and 4 present and analyze games on networks, while chapters 5 and 6 study the generation and diffusion of information in networks.

A game on a network refers to strategic interaction in which players are located at distinct nodes of a network, and the effects of a player's actions on other players are mediated by the structure of the network. The key idea here is that the effect of player i on player j depends on where i is located in the network vis-à-vis j. Networks allow for a natural way of modeling differential influences across players. The idea of local social influence is a well-known instance of this idea. Smoking by a friend is likely to have a much greater effect on a teenager's decision on whether or not to smoke compared with the choices of the people whom she does not knowpersonally. Similarly, a child usually learns the language spoken by her parents and neighbors. In the context of research by firms, similarly, the efforts of research partners have more spillovers on a firm's technological capabilities compared with research of other firms.

There is the issue of whether or not the actions of others increase an individual player's payoffs and her incentives to choose particular actions. Chapter 3 presents simple classifications of strategic effects in terms of positive and negative externalities and strategic substitutes and complements to bring out the range of possible strategic effects.

Over the last two decades, a number of important social and economic phenomena have been studied as arising out of network effects. Some examples of such phenomena are variations in crime, proliferation of research partnerships among firms, the prominence of mavens and opinion leaders, and differences in trust and social cooperation. This body of work has led to a rich set of models, which are taken up in chapters 3 and 4. The aim here is to show how the different models constitute special cases of the framework developed in chapter 3 and how they can be studied by using a set of common techniques. This presentation also highlights a number of interesting open problems.

Imperfect information is a key feature of economic environments. The next two chapters, 5 and 6, study the role that social networks play in the generation as well as the diffusion of valuable information. Chapter 5 considers situations where individual rewards depend only on personal actions, but the payoffs from different actions are not known. In such a situation the experience of friends, colleagues, and acquaintances, namely, the neighbors, is useful since it yields valuable information on alternative actions. The behavior of these neighbors is in turn affected by the choices and experience of their "neighbors" and so on. The chapter develops a theoretical framework to study the effects of network structure on...