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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: 2020-21

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## Module will run

Occurrence Teaching cycle
A Spring Term 2020-21

## Module aims

The module aims to provide students with knowledge and skills to solve a wide variety of optimization problems, such as is commonly encountered in operations research, biological sciences, finance and economics.

The first part of the module is an introduction to linear optimization and solution methods. Emphasis is placed on examples with a realistic flavour from areas like operations research, economics, and finance.  The second part of the module is an introduction to the related theory of games, with emphasis on solution methods based on linear optimization as well as examples arising from biological sciences, finance and economics.

## Module learning outcomes

 After successful completion, the student is able to   Linear optimization State and describe the basic terminology and results concerning linear optimization and linear programming Write a linear program in standard form. Describe duality and its implications for the solutions of linear programs. Use the basic simplex method to solve linear programs and prove its convergence to a solution.   Game theory Describe the basic terminology concerning non-cooperative and cooperative games. State and prove Nash's theorem and use it to solve simple two-player non-cooperative games. State and prove the Core non-emptiness theorem and use it to solve simple cooperative games.   Academic and graduate skills Formulate real-world problems in mathematical terms, solve them using appropriate methods, and interpret the solutions in terms of the original problems. Critically assess assumptions necessary to draw certain conclusions.

## Assessment

Task Length % of module mark
Essay/coursework
Linear Optimization & Game Theory
N/A 40
Online Exam
Linear Optimization & Game Theory
N/A 60

None

### Reassessment

Task Length % of module mark
Essay/coursework
Linear Optimization & Game Theory
N/A 40
Online Exam
Linear Optimization & Game Theory
N/A 60

## 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.

Full printed notes will be provided. The following might be useful for background or additional reading.

 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.

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.