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The University of Southampton
Mathematical Sciences

OR Society 2020 Doctoral Award

Published: 14 January 2021
Marton Benedek
Marton Benedek

Márton Benedek: Computing the Nucleolus of Cooperative Games

Dr Márton Benedek from the University of Southampton received recognition for the 'most distinguished body of research leading to the Award of a Doctorate in the field of Operational Research' for his thesis Computing the Nucleolus of Cooperative Games at the Operational Research (OR) Society's Annual Blackett Lecture in November 2020.

Márton completed his PhD in Mathematics at the University of Southampton 2015-2019, supervised by Professor Joerg Fliege, Head of Department Mathematical Sciences Operational Research, and Tri-Dung Nguyen, Associate Professor in Operational Research/Management Science at the University of Southampton.

Márton Benedek's thesis on cooperative game theory addresses the issue of how decision-makers collaborate by forming coalitions and how the players within a coalition share the benefit in a fair and stable way. A key problem in this area is to compute the nucleolus, which is designed to minimize the dissatisfactions that coalitions could experience under the sharing scheme that is used. However, computing the nucleolus is notoriously difficult because of the large number of potential coalitions that could be formed.

The thesis contains the development of a novel algorithm for computing the nucleolus. It exploits the relationships between primal and dual representations of the problem. Computational tests show that it can handle problems involving over 30 players, whereas previously proposed algorithms are limited to 15 players. Open-source code for different algorithm implementations has been made available. A recent publication has applied the algorithms to model a European gas network with a view to using the nucleolus to assess the bargaining strengths of the different countries in the coalition. ​​​​​​​

The external examiner commented that: "Márton produced a truly remarkable PhD thesis in Operational Research. It has all the features of a fine piece of work in this discipline". Further comments are "the theoretical and algorithmical achievements are significant and influential to the field" and "the descent-based algorithm should be the current benchmark for computing the nucleolus of a general-structure cooperative game".

The George Paterson Memorial Shield
The George Paterson Memorial Shield

After graduating, Márton has continued his career within academia at the Hungarian Academy of Sciences as a researcher, where he is currently working on problems in mechanism design and computation social choice. Additionally, Márton is a teaching assistant at the Corvinus University of Budapest.

Mathematical Sciences Operational Research together with Southampton Business School Data Decision Analytics form the University's Centre for Operational Research, Management Science and Information Systems – CORMSIS.

Statistics and Operational Research at Southampton ranked 37th in the World, 13th in Europe and 8th in the UK (QS World Rankings 2020 by subject)

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