Mathematician Suggested New Approach to Cooperative Game

# Mathematician Suggested New Approach to Cooperative Game

A mathematician from RUDN University developed a matrix representation of set functions. This approach is vivid and easy to check, and it makes the calculations easier. Among other things, the new development can be applied to cooperative game theory.

Specialists in cooperative game theory study methods of complex decision-making in situations with multiple criteria. In such a situation, groups (or coalitions) of players have to come up with a decision that is the most profitable for all of them. Set functions are one of the tools used to work with cooperative game theory. In these functions, the input data are sets of elements that can have different values. Simple explicit questions are quite rare in real life; therefore, the data on different elements can support or neutralize each other. Combinations of elements called coalitions can assume their own values. To work with this apparatus, scientists require an intuitive mathematical language. A mathematician from RUDN University suggested his approach to it

“Our contribution to the mathematical language of cooperative game theory is based on the familiar notions of matrices and vectors. We have developed a formal approach to manipulations with set functions based on linear algebra. Our results can be practically applied to multicriteria decision analysis, group decision-making, operations with dependent goals, economic theories based on cooperative games, and aggregate functions theory,” said Prof. Gleb Beliakov, a Candidate of Physics and Mathematics from RUDN University.

Prof. Beliakov wanted to develop a universal approach that would make expressions equally understandable and convenient for mathematicians, engineers, economists, and specialists in computer science. The best option for it was linear algebra operations based on matrices. Operations with matrices are included in most software packages and are also useful for parallel computations

The scientist obtained matrix expressions by transforming a derived set function expression. A derived function shows how a function transforms when its variables change. Having calculated a derived function, a specialist can give an accurate analysis of a certain situation. In linear algebra, treating an exponential set this way can simplify calculation methods and support effective implementation of many formulae in software. Prof. Beliakov also suggested new formulae for finding the Shapley vector—a version of ‘fair division’ in which the profit of each player is equal to their average contribution to respective coalitions. The new method makes it easier to obtain the Shapley vector in practical applications.

“Set functions are used in economics, decision-making, fuzzy logic, and operational research. An exponential set is a particularly effective tool to model input variables in corporate games. The new apparatus could simplify calculations and support software implementation of many formulae using existing linear algebra packages,” added Prof. Gleb Beliakov from RUDN University.

The results of the work were published in the Information Sciences journal. https://www.sciencedirect.com/science/article/abs/pii/S0020025520308719?via%3Dihub

Visiting Professors View all
03 Nov 2017
Michele Pagano is a graduate of the University of Pisa, a leading scientist, the author of more than 200 publications in international journals, and a participant in many international research projects
2199
30 Jan 2018
The conference on international arbitration, where law students from European universities simulate court proceedings and alternately defend the interests of the respondent and the orator.
957
26 Dec 2022
Tissue architecture, cell organization, biomedical products: RUDN University opens a new research and educational resource center

On October 4, the Research and Educational Resource Center (REC) of innovative technologies of immunophenotyping, digital spatial profiling and ultrastructural analysis (molecular morphology) opened at the RUDN.

34
26 Dec 2022
RUDN scientists suggested how to help the soils of Zaryadye Park

RUDN University scientists conducted a comprehensive soil and environmental survey and took more than 80 soil samples in Zaryadye Park. An assessment of the physicochemical, microbiological, and ecotoxicological properties of soils made it possible to develop recommendations and a plan for the care of soils in analogous landscapes in the park.

50
26 Dec 2022
RUDN University Chemist Creates Nanofilter to Clean Water from Toxic Dyes

RUDN University chemist with colleagues from India and Korea created a nanofilter for water purification from synthetic dyes. The graphene-based composite can quickly remove up to 100% of harmful compounds from water, and it can be used up to seven times without losing efficiency. In addition, the synthesis of the nanofilter itself is economical and environmentally friendly.

36