The games that will change the world: International Conference "Game Theory and Applications" held at St Petersburg University

Game theory is the theory of mathematical models of decision-making in the context of a conflict of parties. It helps to choose the optimal strategies for the behaviour of the stakeholders, taking into account the ideas about the interests of the participants in the conflict, their resources, and possible actions.

There were 119 reports by 199 authors from 19 countries across the world and from 13 regions of Russia submitted to the conference. After the selection, 147 authors delivered their presentations, including 86 presentations by international scientists. In total, 96 sectional reports and 7 plenary reports were presented at the conference.

According to the researchers, the conference is a breakthrough for the science. It has given an impetus to the development of new areas of game theory and its tools. Thus, it promotes more active application of game theory in business, economics, politics, ecology, and other areas of human activity.

The conference was attended by leading international experts in the field of static and dynamic games. Among them are: Tamer Başar (the University of Illinois at Urbana- Champaign, the USA); Vladimir Mazalov (the Institute of Applied Mathematical Research of Karelian Research Centre of the Russian Academy of Sciences, Russia); Abraham Neyman (the Hebrew University of Jerusalem, Israel); Larry Samuelson (Yale University, the USA); Eilon Solan (Tel-Aviv University, Israel); David Yang (Hong Kong Shue Yan University, Hong Kong); and Georges Zaccour (HEC Montréal, Canada) to name just a few.

We talked with Leon Petrosyan, Nikolai Zenkevich, and Artem Sedakov about the significance of the reports and the conference. Leon Petrosyan is Professor, Head of the Department of Mathematical Game Theory and Statistical Decisions and Dean of the Faculty of Applied Mathematics and Control Processes at St Petersburg University. Nikolai Zenkevich is Associate Professor and Head of the Department of Operations Management at St Petersburg University. Artem Sedakov is Professor in the Department of Mathematical Game Theory and Statistical Solutions at St Petersburg University.

Mr Petrosyan, the international conference focuses on the game theory and is held at St Petersburg University for the 16th time. What is special about this conference?

The focus of most conferences on game theory is quite specific. We bring together the main two global areas, i.e. static and dynamic games. There are two professional game theory societies in the world: the International Game Theory Society and the International Society of Dynamic Games. The leaders of both societies made presentations at the conference. Among them are: the President of the Game Theory Society, Professor Larry Samuelson from the USA, and the President of the International Society of Dynamic Games, Russian mathematician, Professor Vladimir Mazalov. Our conference is among the few conferences that bring together scientists of both static games and dynamic games.

Are you satisfied with the outcomes of the conference?

Yes, I am completely satisfied. I can mention at least some of the reports. Among them are: "Identifying the deviator"; "Learning the Mean-Field Equilibrium with Multiple Populations"; "Robust optimisation in stochastic games"; "Equilibrium in Transportation Networks with Externalities"; "Dynamic Pricing and Advertising in the Presence of Strategic Consumers and Social Contagion: A Mean-Field Game Approach"; and "Durable-Strategies Dynamic Games under Uncertainty". For non-specialists, perhaps these titles may seem incomprehensible. This year, without exception, every plenary report showed us a new area in game theory. We can say that these reports are really revolutionary.

Yes, indeed. Few, if any, unprepared readers will understand them. Let’s talk about the practical significance of the conference. Where is game theory applied? Where will new models be applied?

There are many conflicts around us. What is a conflict scientifically? A conflict is a situation in which several people, companies, or countries meet, each with their own interests. Yet none of the participants can succeed on their own. It is necessary to negotiate. How to behave in a situation where the result of making a decision, i.e. income, winning or losing, depends not only on you, but also on the behaviour of other participants? The answer to this question can be provided by the mathematical theory of games. Politicians were the first to see the benefits of the mathematical approach. We can hear the terms, like "optimal solution" or "zero-sum game", quite often in their speeches. This means that the tools of game theory have come into use. Today, game theory or its elements are widely used in assessing public opinion. How? A model of network interaction between stakeholders is built, and key centres of influence on the dissemination of information of a certain type are identified. This is a new aspect of how we can apply game theory, and it is already used widely in practice.

Mr Zinkevich, the game theory is a very practical science, isn’t it?

Game theory in its object of study has always been a practical science. In practice, there are problems of decision-making under conditions of certainty, risk, and uncertainty. Game theory is a special case of decision-making models under uncertainty, when uncertainty is created by the actions of other participants in the process. The models and methods of classical optimisation do not work here. It is necessary to develop mathematical models of stakeholder conflicts that are adequate to real-world problems. There are a huge number of them. It is therefore necessary to study the types, features, and patterns of real conflicts; build specific mathematical models; develop a theory and algorithms for their solution; and check their adequacy in practice. Two types of such applications should be distinguished. The first is applications that follow from the theory of games itself, while the second is applied game-theoretic problems when the object of study is a real practical problem. In this case, game theory is a methodology and tools for solving it. Today, game theory has entered many areas of business, policy, and other areas of decision making.

Could you please tell us more about the importance of game theory for business?

I will give an example from the area that is close to me, i.e. supply chain management, where game theory is now widely used. What is a supply chain? It is a network of companies interacting with each other in the framework of the procurement, creation, distribution, and sale of certain products. All participants have their own interests. The participants are connected by certain relationships and strive to get the maximum result. The question arises: what will lead to such a collective interaction? There are different approaches. Network participants can act independently. It is modelled by a non-cooperative game, and it is mostly about finding a balance. Companies can act centrally, which is modelled by a cooperative game related to the division of the total gain from cooperation. From business to game theory came the concept of coordination, i.e. the motivation of some participants by others to achieve an effective result. Adequate modelling of such conflicts enables us to build effective contracts in an explicit form and give recommendations to companies on the methodology for negotiating their conclusion.

Mr Sedakov, what would you pay attention to when summing up the results of the conference?

All plenary speakers spoke on specific and unique areas of game theory and applications. We could attract a large number of speakers. Among them are experts from different areas of game theory. It was interesting to see the variety of applications of game theory. In other words, we could get acquainted with the reports devoted not only to mathematical theory and the justification of one or another behaviour of the conflicting parties, but also to solutions in the analysis of a practical situation by game-theoretic methods. In particular, we had sections on market behaviour; coalition building; bidding; taxation; anti-corruption; supply chain management; mechanism design; social impact; public goods; machine learning; and experiments. It is quite a wide range of practical application. A total of 31 sessions were organised in various areas of game theory and applications.

Mr Petrosyan, what international game theory centres exist in the world?

In Russia, there are St Petersburg University and the Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences. In the USA, there is Stony Brook. University in New York. In Canada, there is the Université de Montréal There is a strong centre for game theory in Jerusalem. We had two speakers from Jerusalem this year.

Game theory in our country was actually developed at St Petersburg (Leningrad) University. The founder of game theory was Professor Nikolai Vorobyov. He was a research supervisor of a large number of scientists across the Soviet Union and the socialist countries, including my teacher. Professor Vorobyov prepared a whole galaxy of specialists in game theory. We have a very strong team at St Petersburg University. Apart from experienced specialists, many courses are taught by early-career Professors, Doctors of Physics and Mathematics who specialise in this area. The University also offers a master’s programme "Game Theory and Operations Research" in English, which is very popular with international students.

Mr Zenkevich, what was the impetus for holding the conference at St Petersburg University 16 years ago?

In early 2000s, Professor Petrosyan and I attended all major international events on game theory. Among the landmark events was the international conference on game theory in Qingdao in 2002. Just like our conference this year, it was a satellite event of the International Congress of Mathematicians. There was only one game theorist in China, i.e. Hongwei Gao, who was a student of Leon Petrosyan. The organisers invited all the world’s major experts in game theory, including four Nobel Prize winners.

You can see all of them in this picture. From left to right: Robert John Aumann (Israel), 2005 Nobel Prize for Economics; Lloyd Stowell Shapley (1923–2016, the USA), 2012 Nobel Laureate in Economics; Michael Bahir Maschler (1927-2008, Israel); John Forbes Nash Jr (1928-2015, the USA), 1994 Nobel Prize for Economics; party leader of the province of the People’s Republic of China; Leon Petrosyan (Russia); Professor Dov Samet (Israel); Reinhard Justus Reginald Selten (1930-2016, Germany), 1994 Nobel Prize in Economics; David Wing Kay Yeung (Hong Kong); and an academician of the People’s Republic of China.

This event made a strong impression on us, primarily due to the fact that there was a breakthrough in China in the field of training specialists in game theory. We realised the importance of regularly holding such high-quality international events to enable the world’s best scientists to share their latest scientific achievements.

Website of the International Conference "Game Theory and Applications"

Today, for 16 years, the annual conference on game theory at St Petersburg University has been bringing the world’s renowned scientists. I hope that this year’s conference will also serve as an impetus for a breakthrough both in the training of specialists and in game theory itself.

Nobel Prize winners have often participated in our conferences. Last year, Robert John Aumann, an Israeli mathematician and Professor at the Hebrew University of Jerusalem, who received the Nobel Prize in Economics in 2005, spoke for the second time. In 2008 and 2009, we had the outstanding John Nash (the film "A Beautiful Mind" is based on his life) and Reinhard Selten, who shared the 1994 Nobel Prize in Economics, and many other renowned experts. In total, six Nobel Prize winners were plenary speakers.

Mr Sedakov, how actively do students and early-career researchers participate in the conference?

Master’s students are often co-authors of the reports of academic staff. Doctoral students are quite active, too. Students are interested in the reports during the conference, as we have seen.

To encourage early-career researchers in game theory to take part in the conference, the international scientific committee of the conference established "The Best Early-Career Researcher Paper" award. A special committee carefully considered the submitted reports and select a winner. It was Xinmi Li, a postgraduate student at Tsinghua University (Beijing, China) for his work "How do Tom and Jerry Play? A Simple Application of Convex Geometry in Game Theory".

Mr Petrosyan, a beautiful poster is always prepared for the conference. This year, it features not one picture, but many pictures. Why?

Yes, indeed. Our posters always feature scenes of games, i.e. conflicts through the eyes of artists. Usually it’s one picture. When we organise larger gatherings, like this conference, we use many pictures. This year, we have brought together posters from all previous conferences. By the way, the picture for our next event has already been selected.

We started preparing and even chose the dates. The next conference "Game Theory and Management" (GTM2023) will be held on 28 to 30 June 2023 in St Petersburg. We hope to hold the conference in-person.