Cornell Tech

Fall 2019

Instructor: Rafael Pass

Time: M/W 12.30-1.45pm

Place: Bloomberg 131, Cornell Tech

Course Web page: http://www.cs.cornell.edu/courses/cs5854/2019sp/

TAs: Cody Freitag (crf87 at cornell.edu) , Drishti Walli (dw569 at cornell.edu)

Office Hours: W 1.45-2.30 (Bloomberg 255)

The course examines how the computing, economic and sociological worlds are connected and how these connections affects these worlds. Tools from game theory and graph theory are introduced and then used to analyze network structures present in everyday life, with a focus on various types of markets. Topics covered include social networks, web search, auctions, matching markets, and voting.

Basic familiarity with mathematical definitions and proofs. Familiarity with sets, basic probability and basic proof techniques are useful; see Chapters 1,2 and 5 in the following lecture notes: [Pass-Tseng]

There will be 4 homeworks. Homeworks need to be handed in before the beginning of class. Additionally, you have a total of 4 “late-days” that you can use throughout the semester.

You are free to collaborate with other students on the homework (in fact, I
highly encourage you to work in pairs or groups of 3), but **you must turn in your own individually written solution** and you
must specify the names of your collaborators. Additionally, you may make use of
published material, provided that you acknowledge all sources used. Note that
it is a violation of this policy to submit a problem solution that you are
unable to explain orally to a member of the course staff. Submit the homework
online as a pdf. **Problem sets need to be
typed up.**

We will be closely following the material from the book *Networks and
Markets: Game-theoretic Models and Reasoning (The MIT Press, 2019)* (NM
below).

Supplementary material can also be found in the beautiful
book *Networks, Crowds and Markets
(Cambridge University Press, 2010) *by Kleinberg and Easley (KE).* *A complete free on-line version of the
book is available here.

* *

For additional background on sets, proofs and probability theory, please consult the following lecture notes on discrete mathematics: [Pass-Tseng]

**Introduction**[preface in the NM, Chapter 1 in KE]**Game Theory**[Chapter 1 in NM, Chapter 6 in KE]- Definition of a Game
- Dominanted strategies, and iterated deletion procedures
- Nash Equilibrium
- Best response dynamics.

**Graph Theory**[Chapter 2,4 in NM, Chapters 2-4 excl. adv material, 10.1-10.2, 10.6, 13 in KE]- directed, undirected graphs; paths and connectivity
- connected components; the giant component and the internet
- shortest paths and the small world phenomena
- max-flow, min-cut, edge-disjoint paths
- bipartite graphs, maximum and perfect matching, the Hall Marriage problem

**Games on Networks [**Chapters 2,3,4,6 in NM, Chapters 8,19 in KE]- Best-response dynamics as graph traversal; ordinal potential games
- Coordination games on networks (the iPhone/Andoid game);
- Contagion in networks: what makes a node “influential”
- Traffic Networks; Braess “paradox”

**Markets and Auctions on Networks [**Chapter 7,8,9 NM; Chapters 9,10,15 in KE]- Matching markets, market clearing prices.
- Exchange networks
- Auctions and the Vickery-Clark-Grove (VCG) mechanism
- Auctions in matching markets; VCG and the Generalized Second Price (GSP) Auctions; application to sponsored search.

**Mechanisms with Money Transfers: Voting, Matchings and Web search**[Chapters 10,11,12,13,14 in NM]- Voting, strategy-proofness
- Gibbard’s impossibility results
- Single-peaked preferences and the Median Voter theorem
- The House Allocation problem
- Two-sided Matching, The Stable Marriage problem
- The PageRank and Hubs and Authority Algorithms: using links as “votes”
- Manipulation of search algorithms: search engine optimization

**Information and Belief**[Chapters 15,16,17 in NM]- The “Wisdom” of crowds: The Chernoff Bound
- The “Foolishness” of Crowds: Information Cascades; Information Cascades with costly information gathering
- Kripke’s possible worlds models of knowledge; common knowledge
- The Muddy Children Puzze, Can we Agree to Disagree and the No-Trade Theorem
- Common Knowledge of rationality as a characterization of iterated removal of strictly dominated strategies
- The power of higher-order beliefs: Valuation “Bubbles”

**Markets with Network effects**[Chapter 18 in NM]- Price v.s. Demand in markets without network effects
- Price v.s. Demand in markets with network effects; self-fulfilling equilibria
- Markets with asymmetric information: market crashes (the market for lemons) and signaling models