Courses in the Department of Mathematics

MA402: Game Theory I 2009/10

General information about MA402: Game Theory I

Teachers:	Prof Steve Alpern (weeks 1-5) Prof Bernhard von Stengel (weeks 6-10)
Office:	B407, Extension 7620 B412, Extension 6438
E-mail:	s.alpern@lse.ac.uk stengel@nash.lse.ac.uk
Office hours:	(see Office hours page)

Departmental office:	B401, Extension 7925

Lectures:
Tuesdays 12:00-13:00	D1 (Hong Kong Theatre, Clement House)
Tuesdays 16:00-17:00	D1

Classes start on Wednesdays in week 2.
Please check the Timetabling Webpage.

Course format

This is a half unit course, with lectures in the Michaelmas term. There will also be revision lectures in the Summer term.

Note:
This half-unit course Game Theory I MA402 has the same lectures as the undergraduate half-unit course MA301 Game Theory I. The course materials for that course are also quite similar to those for MA402. However, the classes for MA402 are taught by the lecturers, Prof Steve Alpern and Prof Bernhard von Stengel, and homework is marked more comprehensively than for the undergraduate course. The exam for MA402 will be similar in format to MA301, but more difficult. When looking at the past exam papers for MA402, you should note that in the past, MA402 papers were identical to MA301 except that one or two questions on that exam were mandatory. (Past exam papers for MA402 are available below.)

Homework

Exercise sheets will be given out in the second lecture each Tuesday (16:00-17:00), to be submitted into a designated pigeonhole of your class teacher (Prof Alpern or Prof Bernhard von Stengel) for MA300/MA301 on the ground floor of Columbia House, by Tuesday 5pm the following week. This is a sharp deadline, as teachers pick up the homework at that time, and solutions are posted on the web. The topic will be discussed in the next class on Monday or Tuesday. If possible, homework will be marked and return in time for the class. No late homework will be accepted.

Prerequisites

Basic familiarity with calculus, linear algebra and probability. See also the Calendar entry. The course is not available to students who have taken Game Theory (MA300) or Game Theory I (MA301).

Assessment

There will be a formal 2-hour examination in the Summer term.

Textbook

see reading list.

Course description of MA402: Game Theory I

What is game theory?

Game theory studies formal models of conflict and cooperation. The theory started with questions like how to play optimally in chess or poker. The resulting mathematical approaches have been further developed such that they now form a cornerstone of mathematical economics.

Overview

MA402 is an introduction to game theory. At the end of this half-unit course, the student should be familiar with the main concepts of non-cooperative game theory, and know how they are used in modeling and analysing an interactive situation.
The key concepts are:

Players are assumed to act out of self-interest (hence the term "non-cooperative" game theory). This is not identical to monetary interest, but can be anything subjectively desirable. Mathematically, this is modeled by a utility function.
Players should act strategically. This means that playing well does not mean being smarter than the rest, but assuming that everybody else is also "rational" (acting out of self-interest). The game theorist's recommendation how to play must therefore be such that everybody would follow it. This is captured by the central concept of Nash equilibrium.
It can be useful to randomize. In antagonistic situations, a player may play best by rolling a die that decides what to do next. In poker, for example, it may be useful to bet occasionally high even on a weak hand ("to bluff") so that one's opponent will take the bet even if you have a strong hand.

Is this the right course for me?

Prerequisite is some basic familiarity with calculus, linear algebra and probability (see also the Calendar entry). For the mathematical theory of combinatorial games, studied in the beginning lectures, the student should know what the binary system (the base 2 number system) is, e.g. that 1001 in binary is 9 in decimal. The course is mathematical, and theorems will be stated and proved. Nash equilibria with randomized strategies will be described geometrically, which is best understood when knowing the geometry of vectors.

Aims

To familiarise students with formal methods for strategic analysis. To develop the mathematical theory of games as used in economics.

Learning Outcomes

Knowledge of fundamental concepts of non-cooperative game theory. Ability to apply solution concepts to examples of games and to state and explain them precisely. Ability to solve unseen games that are variants of known examples.

Reading list

Complete lecture notes for the course will be made available online.

Historically, some course material for Game Theory I relates to

Fun and Games: A Text on Game Theory by Ken Binmore. D C Heath (1991); ISBN: 0669246034

Playing for Real: A Text on Game Theory

Ken Binmore

The course roughly follows the first 7 chapters of "Fun and Games". The book is rather slow-paced, with lots of examples. A more compact text is

A Course in Game Theory by Martin J. Osborne, Ariel Rubinstein. 352 pages (1994) ISBN: 0262650401
Library number: HB144 O81

A comprehensive, more mathematical book on non-cooperative game theory is

Game Theory : Analysis of Conflict by Roger B. Myerson. Paperback - 584 pages Reprint edition (1997) Harvard Univ Pr; ISBN: 0674341163
Library number: H61.25 M99

Economic applications, which are particularly relevant to Part II of Game Theory (MA300.2), are treated in

A Primer in Game Theory by Robert Gibbons. Paperback - 278 pages (January 1992) Prentice Hall / Harvester Wheatsheaf; ISBN: 0745011594
Library number: HB144 G44

Game Theory by Drew Fudenberg, Jean Tirole. 616 pages (1991) ISBN: 0262061414
Library number: HB144 F95

Past exam papers for this course

Please note: students are advised not to rely too heavily on past exam papers when revising for their exams, as they can only offer a limited indication of what might be covered in a future exam. For further information, please see the guidance here: http://www.maths.lse.ac.uk/examinations_in_mathematics.html#past_papers

Exam paper of 2007 [pdf]