Cooperative game theory: Solving large and uncertain games.

Applications are invited for two fully-funded PhD positions in the Mathematical Sciences (Operational Research Group) and Business School (Management Sciences Group) at the University of Southampton, awarded on the basis of academic excellence to new students who will commence a research programme in Oct 2017. We are looking for applicants interested in the interface of Operational Research and Cooperative Game Theory. Knowledge on Algebraic geometry, numerical computation would be very desirable.

Successful candidates will work with Dr Tri-Dung Nguyen: ([Email Address Removed];http://www.southampton.ac.uk/maths/about/staff/tn6g10.page) and to be co-supervised by another member from Mathematical Sciences or Business School, and possibly by Professor Shmuel Onn from Technion if the project involves computational algebraic geometry: https://iew3.technion.ac.il/~onn/.

Project description: Cooperative game theory is a branch of game theory that offers a conceptually simple and intuitive mathematical framework to model collaborative settings involving multiple decision makers (players). Solutions of cooperative games offer different ways to share the profit or cost among the players in a way that ensures the fairness and stability of the collaboration, while considering the possibility that any subgroup of players has the option to form their own coalition. The focus of this project is on one or several of the following aspects:
(1) Developing operational research techniques for computing solutions of large cooperative games
(2) Developing a new framework for incorporating uncertainty into the classical cooperative games.
(3) Applying cooperative game theory and the findings to real-world applications.
The candidate should have a strong background in operational research. Knowledge on cooperative game theory and computer programming are very desirable. For part (1), we are particularly interested in using ideas from computational algebraic geometry (the Groebner basis & the Graver basis) so any knowledge of these will be a big plus. For part (2), knowledge on stochastic programming and/or robust optimisation is desirable.

REQUIREMENTS
Scholarships will be awarded on a competitive basis. Applicants should have a good degree (equivalent to a UK first-class honours or 2:1 degree) in Operational Research or a related discipline. Applicants should also meet English language requirements (IELTS 6.5 with no subscore lower than 5.5, or equivalent).

APPLICATION PROCESS
Applicants should prepare the following documents: (1) a brief covering letter that describes your reasons for wishing to pursue a PhD in the proposed area; (2) a copy of your CV, including your actual or expected degree class(es), and results of all University examinations; and (3) two academic references. These documents should be sent to Dr Tri-Dung Nguyen ([Email Address Removed]) who will then provide direction for the formal application submission.