Márton Benedek: Computing the Nucleolus of Cooperative Games
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”.