Networks

Course Description

Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form a network over which funds flow and risks are shared. Systemic risk in financial markets often results from the counterparty risks created within this financial network. Food chains, interacting biological systems and the spread and containment of epidemics are some of the other natural and social phenomena that exhibit a marked networked structure.

This course will introduce the tools for the study of networks. It will show how certain common principles permeate the functioning of these diverse networks and how the same issues related to robustness, fragility, and interlinkages arise in several different types of networks.

Lecture Notes

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SES #	TOPICS	SLIDES
1	Introduction to economic, social, and communication networks	Lecture 1(PDF - 1.0MB)
2	Graph theory and social networks Directed and undirected graphs, paths, cycles, diameter, clustering, bipartite graphs. Applications: the web as a directed graph, graphical representation of homophily	Lecture 2 (PDF)
3-4	Branching processes and random graph models Review of branching processes, Erdös-Renyi graphs, degree distributions, phase transitions, connectedness, and giant component. Applications: tipping, six degrees of separation, and disease transmissions	Lecture 3 (PDF) Lecture 4 (PDF)
5-7	Rich get richer phenomena, power laws, and small worlds Preferential attachment, degree distributions, generalized random graphs, and clustering. Applications: firm size distributions, link analysis and web search, PageRank, decentralized search, and navigation	Lecture 5 (PDF) Lecture 6 (PDF) Lecture 7 (PDF)
8	Epidemics and diffusion through networks SIR (susceptible, infected, removed) and SIS (susceptible, infected susceptible) models of diffusion. Applications: spread of information and disease, and genetic inheritance	Lecture 8 (PDF)
9-11	Introduction to game theory Games, strategies, payoffs, extensive and normal forms, and Nash equilibrium. Applications: tragedy of the commons and coordination games	Lecture 9 (PDF) Lecture 10 (PDF) Lecture 11 (PDF)
12	Applications of game theory to networks Modeling network traffic, strategic network formation, negative externalities, Braess' paradox, and potential games. Application: congestion tax in London	Lecture 12 (PDF)
13-14	Evolution, learning, and myopia vs. rationality Evolutionary stable strategies, fictitious play, emergence of Nash equilibrium from rules of thumb, limits of myopic behavior. Application: rules of thumb in traffic	Lectures 13 and 14 (PDF)
15-16	Dynamic and repeated games, and cooperation and trust in networks Subgame perfect Nash equilibrium, repeated games, prisoners' dilemma, repeated games over networks. Application: emergence of cooperation in social networks	Lecture 15 (PDF) Lecture 16 (PDF)
17-18	Network effects, innovation, tipping and contagion Positive externalities, strategic complements, path dependence, diffusion of innovation, and tipping in technology, financial, and product markets. Application: the rise of Microsoft and contagion phenomena	Lectures 17 and 18 (PDF)
19-21	Games of incomplete information Bayes rule, Bayesian Nash equilibria, first and second price auctions, and introduction to social learning. Applications: spectrum auctions, market for lemons, and keyword-based advertising	Lectures 19 to 21 (PDF)
22-23	Social learning in networks Bayesian learning, benefits of copying, herd behavior, informational cascades. Applications: consumer behavior and financial markets	Lectures 22 and 23 (PDF)
24	Decisions in groups Decision making in organizations and societies, social choice, Condorcet jury theorem, and political economy. Application: committee decisions	Lecture 24 (PDF)