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Networks pervade social and economic life, and they play a prominent role in explaining a huge variety of social and economic phenomena. Standard economic theory did not give much credit to the role of networks until the early 1990s, but since then the study of the theory of networks has blossomed. At the heart of this research is the idea that the pattern of connections between individual rational agents shapes their actions and determines their rewards. The importance of connections has in turn motivated the ...
Networks pervade social and economic life, and they play a prominent role in explaining a huge variety of social and economic phenomena. Standard economic theory did not give much credit to the role of networks until the early 1990s, but since then the study of the theory of networks has blossomed. At the heart of this research is the idea that the pattern of connections between individual rational agents shapes their actions and determines their rewards. The importance of connections has in turn motivated the study of the very processes by which networks are formed.
In Connections, Sanjeev Goyal puts contemporary thinking about networks and economic activity into context. He develops a general framework within which this body of research can be located. In the first part of the book he demonstrates that location in a network has significant effects on individual rewards and that, given this, it is natural that individuals will seek to form connections to move the network in their favor. This idea motivates the second part of the book, which develops a general theory of network formation founded on individual incentives. Goyal assesses the robustness of current research findings and identifies the substantive open questions. Written in a style that combines simple examples with formal models and complete mathematical proofs, Connections is a concise and self-contained treatment of the economic theory of networks, one that should become the natural source of reference for graduate students in economics and related disciplines.
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 toform 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 ion 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 know personally. 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 individual choice and learning, over time. The aim is to characterize the properties of social networks that facilitate the diffusion of information about the payoffs from different actions.
Chapter 6 studies the role of social networks in labor market networks. The matching between workers and their employers is characterized by significant imperfections in information. Two types of information are especially prominent in labor markets: the information on job vacancies and the information on the ability of workers. This chapter develops models in which social networks convey information across individual workers and between employers and workers. The aim is to study the different ways in which social networks influence the employment status of individuals and shape the income inequality in a society.
One of the main insights of the first part of the book is that individuals can exploit their network position to their own advantage. Moreover, these advantages are related systematically to aspects of the network structure. In many contexts, the connections that define a network arise out of investments in relationships made by the individual entities themselves. Connections take on different forms and so the nature of investments will vary. In the computer purchase story, for example, the crucial resource is time. I will ask myself whether I should spend time on a personal search or if it would be more worthwhile to spend the time talking to others who may have collected information either personally or through their friends and colleagues. In the context of firms which are deciding on whether to carry out research in-house or to collaborate with other firms, the resources include personnel and financial capital.
These examples suggest two key ideas: one, individuals will trade off the costs and benefits from investments in connections, and, two, an individual's benefits from a connection may actually depend on the connections formed by others. Thus individual decisions on forming connections take place in a context characterized by externalities: if, for example, my friends invest in social connections which enable them to share information with others, then this may make it more attractive for me to invest in connections with them in turn. Similarly, if firms in an industry form connections, then this may alter the gains to a new firm from investing in alliances. So we are led to a study of strategic factors in the formation of networks.
The second part of the book, comprising chapters 7-10, is devoted to the theory of network formation. A game of network formation specifies a set of players, the link formation actions available to each player, and the payoffs to each player from the networks that arise out of individual linking decisions.
The above discussion highlights the possibility that a connection formed between players 1 and 2 may affect the payoffs to other players. This raises the important general issue about who has the power to decide on whether a connection is formed? One of the great attractions of networks is that they are amenable to subtle and quick transformations via local, and small-scale, linking and de-linking activity. This consideration leads us to develop a model in which link formation and dissolution take place at a single-person or at a two-person level and the process is dynamic. A network is said to be strategically stable (or in equilibrium) if there are no incentives for individual players, either acting alone or in groups, to form or delete links and thereby alter the network. Chapter 7 presents this general model and also develops a number of ways of solving games of network formation, which correspond to different levels of individual foresight as well as decision-making power.
The last decade has witnessed a number of exciting developments in the theory of strategic network formation. There have also been a number of attempts to model network formation in specific social and economic contexts. Examples of this work include the formation of information-sharing networks, research collaboration networks among firms, coauthorship networks, labor market networks, buyer-seller networks, and free trade agreements among countries. This body of work addresses three general concerns: (i) What is the architecture of networks that arise in equilibrium? (ii) What is the relation between equilibrium and socially desirable networks? (iii) What are the implications of strategic networking for the distribution of individual earnings? Chapters 8-10 discuss this work and also point out a number of open research questions.
1.2 Networks in Economics
Traditionally, economists have studied social and economic phenomena by using a framework in which interaction is centralized and anonymous. Moreover, prices have been the principal device of coordination among individual actions. The theory of general equilibrium and the theory of oligopoly reflect this approach. In recent years, a growing body of empirical work has argued that this approach is inadequate for an understanding of a number of phenomena such as the diffusion of innovations, variations in crime, differences in trust and cooperativeness, peer effects in academic performance, the proliferation of research alliances among firms, and the extensive use of personal contacts by both employers and workers in labor markets. I now discuss empirical patterns in the diffusion of innovation to bring out the central role of the pattern of interaction.
Technological change is central to economic growth and social development. The process of technological change is complicated and involves many steps starting from basic research and going on to wide-scale adoption. But it is generally agreed that wide diffusion is important for the full gains of a new technology to be realized. This rate of diffusion, however, seems to vary greatly. Consider the following examples:
It took a millennium for the water mill to be widely adopted in Europe; it is felt that the main reason for this slow Pace of diffusion was the absence of significant mobility during pre-medieval and medieval times. The spread of new hybrid seeds has been central to the increase in agricultural productivity over the past century. The classical work of Ryan and Gross (1943) documents that hybrid corn seeds were adopted over a period of several years in the early twentieth century, in the United States. Moreover, diffusion of these seeds displayed clear spatial patterns: initially, a small group of farmers adopted the seed, followed by their neighbors adopting it, and this was followed by the neighbors of the neighbors adopting it, and so on. The period before the first prescription of a new medicine by doctors within the same city can vary widely. For instance, Coleman, Katz, and Mentzel (1966) found that this period ranged from six months to three years within a Midwestern town in the United States and also observed that a significant part of this variation is explained by the differences in social connections across doctors. The facsimile technology was available in 1843 and AT&T introduced a wire photo service in 1925. However, fax machines remained a niche product until the middle of the 1980s. Since then there has been an explosion in the use of fax machines.
The research on the determinants of diffusion suggests that the critical factor in the diffusion of a new technology is the uncertainty about its profitability. Information from governments and firms will alleviate this uncertainty. However, if the technology in question is complicated and involves substantial resources, such as adoption of crops or prescription of medicines, then it is clear that an individual is likely to place much greater faith in information from close friends, colleagues, and neighbors, and others in a similar decision situation. Moreover, in some instances, such as with fax machines, an individual's payoffs from adopting the product depend on whether others with whom she interacts frequently adopt the same product. Thus the patterns of interaction between individuals are likely to play a key role in shaping individual choice and therefore shaping innovation at an aggregate level as well.
This example allows us to draw out two important theoretical points. The first point is about the descriptive appeal of social interaction: in many economic contexts, social interaction between individual entities is clearly present. The second point is about the functional aspect of social interaction: such interaction facilitates the transmission of valuable information. This suggests that the structure of interaction may be viewed as an instance of informal institutions that supplement formal markets in the presence of imperfect or asymmetric information. To the extent that information imperfections are pervasive, this suggests a potentially major role for patterns of connections in shaping economic activity.
These considerations suggest an ambitious research program which combines aspects of markets (e.g., prices and competition) along with explicit patterns of connections between individual entities to explain economic phenomena. In the last decade considerable progress has been made in this research program. The present book provides an overview of this work.
The research on networks reported in this book is related to, but distinct from, two other strands of research in economics: the study of network industries (such as airlines, telecommunications, electricity, software industries) and the empirical work on social interactions. It is important at the very outset to clarify this distinction. In the literature on network industries, profit-maximizing firms own and control the functioning of their network; by contrast, a large part of this book is concerned with social and economic networks where there is no single entity who owns the network. The focus is in developing a framework where individual entities create their own links with others and this shapes the structure of economic and social interaction.
Excerpted from Connections by Sanjeev Goyal
Copyright © 2007 by Princeton University Press. Excerpted by permission.
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Chapter 1: Introduction 1
1.1 Themes 1
1.2 Networks in Economics 4
1.3 The Economic Approach and Other Subjects 7
1.4 A Note on Style 8
Chapter 2: Networks: Concepts and Empirics 9
2.1 Introduction 9
2.2 Concepts 9
2.3 Properties of Empirical Networks 20
Chapter 3: Games on Networks 25
3.1 Introduction 25
3.2 General Model 27
3.3 Applications 34
3.4 Discussion of Two Assumptions 49
3.5 Concluding Remarks 53
3.6 Appendix 55
Chapter 4: Coordination and Cooperation 63
4.1 Introduction 63
4.2 Coordination Games 66
4.3 Games of Conflict 75
4.4 Concluding Remarks 80
4.5 Appendix 81
Chapter 5: Social Learning 87
5.1 Introduction 87
5.2 Theoretical Framework 89
5.3 Learning from Neighbors 94
5.4 Related Themes 102
5.5 Concluding Remarks 104
5.6 Appendix 105
Chapter 6: Social Networks in Labor Markets 113
6.1 Introduction 113
6.2 The Social Transmission of Job Information 116
6.3 Adverse Selection and Referrals 120
6.4 The Use of Social Networks: Empirical Evidence 124
6.5 Concluding Remarks 128
6.6 Appendix 128
Chapter 7: Strategic Network Formation: Concepts 143
7.1 Introduction 143
7.2 One-Sided Links 147
7.3 Two-Sided Links 150
7.4 Efficiency and Equity 158
7.5 Concluding Remarks 158
7.6 Appendix 159
Chapter 8: One-Sided Link Formation 163
8.1 Introduction 163
8.2 A Simple Model of Link Formation 165
8.3 Extensions 171
8.4 Experiments and Empirical Regularities 182
8.5 Research in Other Subjects 185
8.6 Concluding Remarks 188
8.7 Appendix 188
Chapter 9: Two-Sided Link Formation 199
9.1 Introduction 199
9.2 Network Formation: Four Applications 200
9.3 Stability and Efficiency 215
9.4 Unequal Degrees and Payoffs 221
9.5 Concluding Remarks 227
9.6 Appendix 229