CS40915 Algorithmic Game Theory
Introductory description
The focus of the module is on algorithmic and computational complexity aspects of gametheoretic models.
Module aims
To familiarise students with formal methods of strategic interaction, as studied in game theory. One of the aims will be to give a flavour of current research and most recent advances in the field of algorithmic game theory.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Game models: Strategic form, extensive form, games of incomplete information (eg auctions), succinct representations, market equilibria, network games, cooperative games;
Solution concepts: Nash equilibria, subgame perfection, correlated equilibria, Bayesian equilibria, core and Shapley value;
Quality of equilibria: Price of anarchy, price of stability, fairness;
Finding equilibria: Linear programming algorithms, LemkeHowson algorithm, finding all equilibria;
Complexity results: Efficient algorithms, NPcompleteness of decision problems relating to set of equilibria, PPADcompleteness;
Some parts of the module will be researchled, so some topics will vary from year to year.
Learning outcomes
By the end of the module, students should be able to:
 Understand the fundamental concepts of noncooperative and cooperative game theory, in particular standard game models and solution concepts.
 Understand a variety of advanced algorithmic techniques and complexity results for computing gametheoretic solution concepts (equilibria).
 Apply solution concepts, algorithms, and complexity results to unseen games that are variants of known examples.
 Understand the state of the art in some areas of algorithmic research, including new developments and open problems.
Indicative reading list
Osborne and Rubinstein, A Course in Game Theory;
Roughgarden, Selfish Routing and the Price of Anarchy;
Nisan, Roughgarden, Tardos and Vazirani (eds), Algorithmic Game Theory;
Selected research papers.
Subject specific skills
Advanced algorithmic techniques;
Transferable skills
Problem Solving;
Communication skills
Study time
Type  Required 

Lectures  30 sessions of 1 hour (20%) 
Seminars  9 sessions of 1 hour (6%) 
Private study  111 hours (74%) 
Total  150 hours 
Private study description
private reading and revision
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D4
Weighting  Study time  

Coursework 1  5%  
question sheet 1  peer assessed 

coursework 2  15%  
question sheet 

Inperson Examination  80%  
CS409 examination

Assessment group R1
Weighting  Study time  

Inperson Examination  Resit  100%  
CS409 resit paper

Feedback on assessment
Written comments and marks.
Prerequisites
Students must have studied the material in CS260 or equivalent relevant content.
Courses
This module is Optional for:
 Year 5 of UCSAG504 MEng Computer Science (with intercalated year)
 Year 1 of TCSAG5PD Postgraduate Taught Computer Science

UCSAG503 Undergraduate Computer Science MEng
 Year 4 of G503 Computer Science MEng
 Year 4 of G503 Computer Science MEng
 Year 4 of UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
This module is Option list A for:
 Year 5 of UCSAG504 MEng Computer Science (with intercalated year)

RMAAG1PG Postgraduate Research Mathematics of Systems
 Year 1 of G1PG Mathematics of Systems
 Year 1 of G1PG Mathematics of Systems
 Year 1 of TMAAG1PF Postgraduate Taught Mathematics of Systems

UCSAG503 Undergraduate Computer Science MEng
 Year 4 of G503 Computer Science MEng
 Year 4 of G503 Computer Science MEng
 Year 4 of USTAG304 Undergraduate Data Science (MSci)
 Year 4 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 5 of UCSAG4G4 Undergraduate Discrete Mathematics (with Intercalated Year)

UMAAG100 Undergraduate Mathematics (BSc)
 Year 3 of G100 Mathematics
 Year 3 of G100 Mathematics
 Year 3 of G100 Mathematics
 Year 3 of UMAAG103 Undergraduate Mathematics (MMath)
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year
This module is Option list B for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 4 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe