What is game theory? what is network theory? games on networks; empirical network; power law distributions.
Games on networks
This lecture focuses on strategic interaction that take place on networks. Part 1 overviews structural properties of empirical networks. Part 2 introduces a mathematical framework and notions of equilibria for thinking about strategic interaction between multiple players. Part 3 focuses on applications of game theory, including modeling network traffic, link analysis and web search and voting processes.
The best for the group comes when everyone in the group does what’s best for himself and the groupJohn Nash
Overview
Instructor: Jorge Finke
Office hours: Th 5:00-6:00pm
Level: graduate
TA: TBD
Schedule
| Week starting… | Lectures |
|---|---|
| Jan 25 | Lec 1 - Introduction |
| Feb 1 | Lec 2 - Strong and weak network ties, clustering, and bridges |
| Feb 8 | Lec 3 - Homophily and community structures |
| Feb 15 | Lec 4 - Representations of a game |
| Feb 22 | Lec 5 - What is a game? |
| Feb 29 | Lec 6 - Best responses and dominant strategies |
| Mar 7 | Lec 7 - Nash equilibrium |
| Mar 14 | Lec 8 - Multiple Nash equilibria |
| Mar 21 | — spring break — |
| Mar 28 | Lec 9 - Mixed strategies |
| Apr 4 | Lec 10 - Pareto optimality |
| Apr 11 | Lec 11 - Project 1 presentations |
| Apr 18 | Lec 12 - Modeling network traffic |
| Apr 25 | Lec 13 - Link analysis and web search |
| May 2 | Lec 14 - Voting processes |
| May 9 | Lec 15 - Project 2 presentations |
Assignments
Homework 1 (due Feb.18th, 2016)
Homework 2 (due March 3rd, 2016)
Homework 3 (due May 19th, 2016)
Project 1 (due April 14th, 2016)
Project 2 (due June 10th, 2016)
Lessons
Transitivity and strong triadic closure
Small-world networks; transitivity; strong and weak network ties; strong triadic closure.
Homophile, community structures, and sign networks
Homophile; mechanisms underlying homophile; community structures; positive and negative relationships
Representations of a game
What is a game? Reasoning about strategic behavior; the extensive and normal form of a game; best responses and dominant strategies; the Nash Equilibrium; multiple Equilibria; coordination Games
Mixed strategies
Mixed strategies; Pareto and social optimality; weakly donated v. strictly dominated Strategies; dynamic games
Fundamental Theorem of game theory
The Fundamental Theorem of game theory; how to find find Nash equilibria
Evolutionarily stable strategies
Evolutionary game theory; fitness as a result of interaction; evolutionarily stable strategies
Traffic networks
Games on networks: traffic networks
Auctions
Types of auctions; ascending-bid; descending-bid; first-price sealed-bid; second-price sealed-bid; modeling second-price auctions as games
Bargaining in social networks
Power in social networks; bargaining Nash equilibrium; the ultimatum game
Web search
The structure of the web; link analysis and web search; PageRank
Multiple-item auctions
Matching markets; perfect matching; market-clearing prices (multiple-item auctions); multiple-item v. single-item auctions
Course review
Review of course material.
Sponsored markets
Advertising as a matching market; the VCG price auction; encouraging truthful bidding