## MAS348 Game Theory

 Semester 1, 2021/22 10 Credits Lecturer: Dr Moty Katzman Home page Timetable Reading List Outcomes Teaching Methods Assessment Full Syllabus

The module will give students an opportunity to apply previously acquired mathematical skills to the study of Game Theory and to some of its applications in Economics.

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)
No other modules have this module as a prerequisite.

## Outline syllabus

1. Formal definition of games both in strategic for and in sequential form.
2. Solution of games by elimination of dominated strategies.
3. Pure and mixed Nash equilibria of games.
4. Nash Bargaining.
5. Application of game theoretical techniques to solve real-life problems, e.g., in Economics.
6. Solution of sequential games using backward induction.
7. Translation games in normal form to sequential form and viceversa applying the concept of information sets and sub-game perfect Nash equilibria.
8. Repeated games and their Nash equilibria.
9. Bayesian games and their equilibria.

## Learning outcomes

By the end of the unit, a candidate will be able to demonstrate: 1. An understanding of the notions of strategy, both pure and mixed. 2 An ability to solve games by examining dominated strategies and minimax strategies. 3 An understanding of the technique of backward induction and its application for the solution of games. 4 An ability to solve problems originating from Economics by using game theoretical methods.

## Teaching methods

There will be two formal lectures per week, which will involve the formulation of new theory and worked examples. Students will work through set exercises, and also submit homework for marking, although this will not be part of the formal assessment.

20 lectures, no tutorials

## Assessment

One 2.5 hour exam.

## Full syllabus

Cooperative games- pure strategies (3 lectures)
Nash equilibria in Economics: monopolies, duopolies and oligopolies (2 lectures)
Cooperative games- mixed strategies (3 lectures)
Sequential games (5 lectures)
Repeated games (4 lectures)
Bayesian games (3 lectures)

## Reading list

Type Author(s) Title Library Blackwells Amazon
B K. Binmore Playing for Real: Game Theory 519.3 (B) Blackwells Amazon
B M. J. Osborne An introduction to game theory 519.3 (O) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.