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Mathematical Game Theory (MAST90137)
Graduate courseworkPoints: 12.5Not available in 2024
Overview
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Game theory is a branch of mathematics where the interactions between rational decision makers (players) are modelled and analysed. Game theory can broadly be divided into the study of noncooperative games and cooperative games. For noncooperative games we study two-player games, games in extensive form, games of perfect and imperfect information, games with complete and incomplete information, games with chance moves, repeated games, and Bayesian games. To analyse these games we introduce the concepts of Nash equilibria, evolutionary stable strategies, subgame perfect equilibria, and belief spaces. For cooperative games we study coalitional games with transferable utility, and introduce the concepts of coalitions, characteristic functions, the core, the Shapley value, the nucleolus, and dual games. We prove the well known Bonderava-Shapley theorem which gives conditions for the nonemptyness of the core. This subject provides a rigorous mathematical treatment of game theory, and will include applications selected from queueing theory, biology, population dynamics, resource allocation, auction theory, political science, and military applications.
Intended learning outcomes
After completing this subject, students should be able to:
- Demonstrate an understanding of the fundamental concepts and techniques for modelling and analysing noncooperative and cooperative games;
- Demonstrate their developed skills needed to solve problems in game theory from a rigorous mathematical perspective;
- Analyse and solve problems in noncooperative and cooperative game theory;
- Develop and analyse game theoretical models in areas where game theory can be applied; and
- Pursue further studies in game theory and related areas.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- Problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- Analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- Collaborative skills: the ability to work in a team; and
- Time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 13 April 2024
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30022 | Decision Making | Semester 2 (On Campus - Parkville) |
12.5 |
Or equivalent.
Corequisites
None
Non-allowed subjects
None
Recommended background knowledge
MAST20004 Probability or MAST20006 Probability for Statistics, and MAST20018 Discrete Maths and Operations Research, or equivalent.
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 13 April 2024
Assessment
| Description | Timing | Percentage |
|---|---|---|
Continuing assessment of up to 40 hours work, worth 40% of the mark, throughout the semester
| Throughout the teaching period | 40% |
Written examination
| During the examination period | 60% |
Last updated: 13 April 2024
Dates & times
Not available in 2024
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 13 April 2024
Further information
- Texts
Prescribed texts
Recommended texts and other resources
Maschler, M., Solan, E., and Zamir, S. Game Theory, Cambridge University Press, 2013
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 13 April 2024