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# Linear Optimization & Game Theory - MAT00050H

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• Department: Mathematics
• Module co-ordinator: Prof. Jacco Thijssen
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2021-22

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## Module will run

Occurrence Teaching cycle
A Spring Term 2021-22

## 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 optimization. Topics to be discussed include Nash equilibria
in strategic-form games and the core of coalition-form games.

Throughout, an emphasis is placed on modelling realistic situations from areas like operations
research, finance, and economics. In addition, attention will be paid to the reporting of the analysis of
such models in the business context.

## 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 describe the fundamental and duality theorems.

Game theory

• Describe the basic terminology concerning strategic-form and coalitional games.
• State and describe the Nash theorem, and compute Nash equilibria in strategic-form games.
• Compute Core allocations in coalitional 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 M-level version. During Weeks 5 and 6 this module shows (via videoed lectures) how to use Excel (or similar) to implement the algorithms computationally, whilst the M-level version of this module continue with lectures on the theoretical development and proofs. In Week 9 and 10 there is a similar divergence between the two modules, where students on this module learn about coalitional games, whilst the M-level students continue the lectures with more theoretical material, in particular a proof of the Nash theorem.

## Assessment

Task Length % of module mark
Online Exam
Linear Optimization & Game Theory
3 hours 100

None

### Reassessment

Task Length % of module mark
Online Exam
Linear Optimization & Game Theory
3 hours 100

## Module feedback

 Marked coursework returned and discussed in examples classes. Examination result delivered in Week 10 of SuT, with model solutions and examiner’s comments available earlier.

## Indicative reading

• Lecture notes
• Luenberger, D.G. and Y. Ye (2008), Linear and Non-Linear Programming, 3 rd edition, Springer.
• Maschler, M., E. Solan, and S. Zamir (2020), Game Theory, 2 nd edition, Cambridge University Press.
• Osborne, M. and A. Rubinstein (1994), A Course in Game Theory, MIT Press.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.