The course will cover some basic concepts in graph theory, and probability theory. Based on these concepts, it will then present the main models in the theory of random graphs and their use in network formation. It will introduce some basic concepts in game theory and, based on them, it will study some different models of network formation. Then it will cover some games on networks, among them routing games, and it will explore existence and efficiency of equilibria. A part of the course will be devoted to matching theory and various applications. The course will deal with online auctions and web search. The issue of information and its transmission on networks will be examined in detail.

The following topics will be covered:
Basic concepts of graph theory
Basic probability and random graphs and network formations
Basic concepts of game theory. Normal-form games and extended-form games. Nash equilibria and subgame perfect equilibria
Strategic network formation
Games on networks, Routing games. Potential games. Price of Anarchy and Price of Stability.
Matching theory and its applications.
Auctions
World wide web
Information transmission on networks and cascades
Small world phenomenon
Epidemics
Markets and information

Useful textbooks
Easley, D. and Kleinberg, j., Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press, 2010.
Jackson, M.O., Social and Economic Networks, Princeton University Press 2010.
Newman, M. Networks, 2nd Ed., Oxford University Press, 2018.
Barabási, A-L, Network Science, Cambridge University Press, 2016.
Pass, R., A Course in Networks and Markets: Game-Theoretic Models and Reasoning, MIT Press, 2019