An important milestone: mathematicians from St Petersburg University make a significant contribution to the study of game theory

According to the authors of the article, the first person to study this subject at St Petersburg University was the great mathematician Leonard Euler. He was one of the founders of the calculus of variations. It is a branch of mathematics that laid the foundations for optimisation theory and the main tool of mathematical game theory, which studies functions. Mathematicians from St Petersburg University emphasise that this work lays an indispensable foundation of optimisation for the development of mathematical game theory.

An article on the history of the study and development of game theory at St Petersburg University was published in the International Game Theory Review to mark the University's 300^th anniversary.[ЕЛ1] 

Formal studies of game theory, however, began in the 1950s. The first scientific paper in the USSR was published in the Vestnik of Leningrad State University by Nikolai Vorobyov, a graduate of Leningrad State University, under the title ‘Controlled Processes and Game Theory’.

‘Professor Vorobyov also organised a series of scientific seminars on game theory, which for a long time was the only centre for the development of this branch of applied mathematics in the country. At the seminars, lecturers, students and scientists gave presentations, discussed specific problems in game theory and prepared for field-specific conferences. The participants in the seminars were famous mathematicians of their time, representatives of many countries: Georgia, Armenia, Lithuania, the German Democratic Republic, China, North Korea and others,’ the scientists from St Petersburg University noted in the article.

It is impossible not to mention the pioneering work of the lecturers of the Mathematics and Mechanics Faculty of the University in solving one of the main problems of game theory – the construction of the optimality principle. Olga Bondareva and her students Tatiana Kulakovskaia, Natalia Naumova and others made a great contribution to this research.

We should also mention the so-called differential or dynamic games, which are mathematical models of conflicts developing over time. Leon Petrosyan, at that time a doctoral student in the Mathematics and Mechanics Faculty of Leningrad State University and now a professor at St Petersburg University, defended the first candidate’s dissertation on this subject in the USSR.

Scientists of the leading schools of thought in Russia are still actively engaged in the study of differential games, which indicates the relevance of this area of study.

A huge contribution to the study of game theory was made by Leningrad State University mathematicians in relation to optimal control problems in the presence of uncertainty. Explicit analytical solutions have been found for the pursuit game ‘with a lifeline’, the pursuit game in a half-plane, the game with multiple pursuers and one escapee, and the game with a non-zero sum of one pursuer and multiple escapees.

Also important was the study of cooperative games, for which researchers from the University proposed a sophisticated theory that ensures the stability of the system. This theory includes rigorous formulations of typical problems, conditions for their regularisation, methods for constructing the necessary controls, and issues of correctness and feasibility of the proposed solutions.

Later, methods and strategies for dynamic games with incomplete information were put forward at St Petersburg University. For example, for search-type games, mathematicians from St Petersburg University proposed several methods that later formed the basis for a number of applied papers on the development of new game-theoretic methods for searching and tracking moving objects.

Together with specialists from the Karelian Research Centre of the Russian Academy of Sciences (Petrozavodsk), the scientists from St Petersburg University studied a wide class of dynamic and evolutionary games arising in problems of animal behavioural ecology.

The Euler International Mathematical Institute at St Petersburg, a world-class international mathematical centre, was established in 2019 as a consortium of St Petersburg University and the St Petersburg Department of the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. The world-class mathematical centre ‘The Euler Mathematical Institute’ focuses on fundamental mathematical research and its interaction with such applied research from different areas of industry for which there are no standard approaches.

Game theory research at St Petersburg University continues today. In 2000, the Centre for Game Theory was established. It is headed by Leon Petrosyan, Professor of St Petersburg University, and David Yang, Professor of the University of Hong Kong and Professor Emeritus of St Petersburg University. Together they have developed and constructed principles of optimal behaviour in conflict systems that guarantee the sustainable development of such systems over time, which is particularly important from an application point of view. The researchers have analysed and derived strategies for a separate class of dynamic games – dynamic games with stable strategies. Additionally, the Department of Mathematical Game Theory and Statistical Decisions at St Petersburg University continues to host all-Russian and international conferences, symposia and congresses in this field of applied mathematics, and the University's scientists show outstanding results.

Staff, graduates and students of St Petersburg University have published more than 1,500 papers on the subject of mathematical game theory in peer-reviewed journals. Lecturers who are graduates of St Petersburg University have twice been elected presidents of the International Society of Dynamic Games. Professor Leon Petrosyan was awarded the highest world prize in the field of dynamic games – the I Martin Isaacs Prize – for his outstanding contribution to the development of differential game theory.