Studying at York
Linear Optimization & Game Theory - MAT00087M
- Department: Mathematics
- Module co-ordinator: Prof. Jacco Thijssen
- Credit value: 10 credits
- Credit level: M
- Academic year of delivery: 2022-23
- See module specification for other years: 2021-22
Related modules
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Spring Term 2022-23 |
Module aims
The first part of the module provides students with knowledge and skills to solve a wide variety of linear optimisation problems that are commonly encountered in operations research, finance and economics. The theory of linear optimisation will be discussed together with solution methods, such as the simplex method. Students are given the opportunity to solve and analyse realistic, though simplified, models using widely-used spreadsheet software.
The second part of the module is an introduction to the theory of games, with a focus on those concepts that have a close link with linear optimisation. Topics to be discussed include Nash equilibria in strategic-form games and the core of coalition-form games.
Throughout, an emphasis is placed on the mathematical development of the theory of linear optimisation and the theory of games. Concepts from real analysis and metric spaces will be used to prove some of the important theorems of these theories.
Module learning outcomes
After successful completion, the student is able to
Linear optimisation
- State and describe the basic terminology and results concerning linear optimisation.
- Describe the basic simplex method and use it to solve linear programs.
- State and prove the fundamental and duality theorems of linear optimisation.
Game theory
- Describe the basic terminology concerning strategic-form games.
- State and prove the Nash theorem, and compute Nash equilibria in strategic-form games.
Academic and graduate skills
- Formulate real-world problems in mathematical terms, solve these using appropriate methods, and interpret the solutions in terms of the original problems.
- Critically assess mathematical theories.
Module content
The first few lectures are shared with the H-level version. During Weeks 5 and 6 this module continues with lectures on the theoretical development and proofs, whilst the H-level module shows (via videoed lectures) how to use Excel (or similar) to implement the algorithms computationally. In Weeks 9 and 10 there is a similar divergence between the two modules, where students on this module continue the lectures with more theoretical material, in particular a proof of the Nash theorem, whilst the H-level students learn more about the applications of coalitional games.
Indicative assessment
| Task | Length | % of module mark |
|---|---|---|
| Closed/in-person Exam (Centrally scheduled) Linear Optimization & Game Theory |
2 hours | 100 |
Special assessment rules
None
Indicative reassessment
| Task | Length | % of module mark |
|---|---|---|
| Closed/in-person Exam (Centrally scheduled) Linear Optimization & Game Theory |
2 hours | 100 |
Module feedback
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
- Lecture notes
- Luenberger, D.G. and Y. Ye (2008), Linear and Non-Linear Programming, 3rd edition, Springer.
- Maschler, M., E. Solan, and S. Zamir (2013), Game Theory, Cambridge University Press.
- Osborne, M. and A. Rubinstein (1994), A Course in Game Theory, MIT Press.