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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
  • See module specification for other years: 2019-20 2021-22 2022-23

Related modules

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

Special assessment rules

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.

Indicative reading

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.