On June 23-25, 2021, the Fifteenth International Conference "Game Theory and Management" (GTM2021), organized by St. Petersburg University in partnership with the International Society of Dynamic Games, will take place. We talked about the benefits of the conference of mathematicians for business and public administration, connection with psychology and game plots of masterpieces of world painting with the co-chairman of the program and organizing committees, Associate Professor of the Department of Operations Management of the Business School, Academic Director of the Master of Corporate Finance program Nikolay Zenkevich.

  

Please tell us about the role of the conference in the system of thematic international scientific meetings. Are there any specificities this year?

This year, the fifteenth research conference "Game Theory and Management" will take place and for the second time it will be held online. Our conference is international, it traditionally brings together representatives of about 20 countries. Online is the only way to bring everyone together amid pandemic constraints. This is not an easy task but after all, 93 reports have been announced, which will be delivered by people living in different time zones. All these nuances must be taken into account.

By the way, it is interesting that the Nobel laureate in economics Robert Aumann, a keynote speaker of this year, also spoke at our debut conference in 2007. He is one of the first experts in the world to receive the Nobel Prize for results in game theory. He is already over 90 years old and, if not for the online format, his performance could hardly have taken place.

If we talk about the recognition of our conference in the international academic community, it should be noted that there are two associations of specialists in this field in the world — the International Society of Game Theory and the International Society of Dynamic Games. So, we are recognized by representatives of both. Both societies annually publish detailed information about the next conference on their website. However, the official co-organizer of the conference, along with St. Petersburg University, is the Russian branch of the International Society for Dynamic Games.

The 15th International Conference "Game Theory and Management" is organized by St. Petersburg University (Faculty of Applied Mathematics - Management Processes and the Graduate School of Management) in cooperation with the International Society of Dynamic Games. A keynote  plenary presentation on the synthesis of classical theory and behavioral approaches in economics will be delivered by the Nobel Prize laureate (“For expanding understanding of conflict and cooperation problems through analysis in the framework of game theory”) Professor Robert Aumann (Israel). The presentation of the Dean of the Faculty of Applied Mathematics of St. Petersburg University, Professor Leon Petrosyan, co-organizer of the conference and one of the world's leading experts in game theory in Russia, will be devoted to differential games on networks.. The plenary reports of outstanding researchers David Young (Hong Kong) and Ehud Kalai (USA) are also of great interest.

  

How interesting can the conference be to non-academic people? Still, mathematics, theory ... are so complicated.

There are difficulties in understanding. The apparatus of game theory is rather complicated, but it is a specialized conference for academic society. Even trained professionals need to be willing to grasp the essence of the issues discussed. However, the peculiarity of our conference is that we are talking not only about the problems of game theory. To the same extent, we are interested in its application in management: both in the management of companies, organizations, the state, in solving economic and environmental problems, any problems of a conflict nature are of interest. This significantly expands our horizons and makes the conference fundamental and mathematical, interesting to a wide range of persons and to business.

    

You are talking about business. But are mathematicians, especially applied ones, objectively interested in attracting specialists from other fields?

Our main problem, and we honestly admit it, is the gap between advances in the development of mathematical methods, in particular the theory of games, and its application. For practical applications, it is necessary that there are mathematical models adequate to real problems. But mathematicians, despite the fact they see potential opportunities, cannot set the task of building an adequate applied model. Practitioners, on the other hand, are not able to fundamentally solve their problem, because they cannot use the mathematical apparatus, for example, of game theory.

One of the goals of our conference is to close this gap so that managers at least have an idea of ​​the available opportunities and are eager to use them. Popularization and development of new directions, the formulation of relevant topics is one of the key tasks of the conference. Ideally, we aim to become a platform where business and academics can meet. It is important that an interested community of specialists and practitioners is formed around the conference.

  

It is known that game theory allows the use of social psychology in modeling situations. How do you manage to combine exact and social science?

On the one hand, there are major differences. If we are talking about the classical mathematical game theory based on the approach fixed by its founders John von Neumann and Oskar Morgenstern in the middle of the last century, then it assumes the rational behavior of the participants. The psychological analysis of the conflict is based on the fact that a person is a being who often behaves in an irrational manner. However, this does not mean that there are no intersections between these sciences. In modern game theory, an approach of partial and bounded rationality is developed in relation to the analysis of conflicts, the results of which lead to appropriate game models. In particular, such a subclass is known — reflexive games, which are developed specifically to take into account the psychological characteristics of the conflict.

It should be noted that advances in convergence of economic theory, game theory with psychology and sociology are supported by the academic community. For example, French economist Jean Tirol received the 2014 Nobel Prize for his “analysis of market power and regulation”. In particular, the results were considered based on the psychological approach in the development of economic theory. Earlier, in 2007, the American scientist Roger Myerson became a Nobel laureate in economics, including for the use of game theory in political science when studying and comparing the work of electoral systems.

Traditionally, the most popular areas of application of game theory are economics and management, political science and international relations, since decisions within these areas are of a conflicting nature. An even greater demand for the application of game theory is in the analysis of military conflicts.

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

Traditionally, conflict analyzation based on game theory, demand the seek of answers to the following questions:

• What is the conflict model (what is the game)?

• Which solution should be considered optimal?

• How to find the optimal solution?

Recently, the answer to the question of the design of the decision making mechanism has been of great interest in research:

• How can the rules of the game be changed so that the optimal solution leads to the desired outcome of the conflict?

  

It can be assumed that states may be interested in the development of game theory as because it can be used precisely in military affairs.

It is worth recognizing that the main motivation and engine for the development of game theory, especially dynamic ones, during the Soviet period was indeed the need to analyze various military conflicts. But I must say that from the point of view of game theory, these are very “simple” conflicts, the so-called antagonistic ones. In such a bilateral relationship, the gain of one player in any situation is equal to the loss of the other. Therefore, there can be no agreements and compromises between the participants.

Now the situation has changed. Today we are working in a wide range of different areas of game theory. We model non-antagonistic conflicts for different systems: economic, managerial, environmental, social, human-machine, automatic.

The answer to the question of where game theory is more useful depends on where and who undertakes to apply it. It is useful wherever it is skillfully used.

    

Have there been cases involving mathematicians - experts in game theory - in the examination of specific situations at the state level?

There are such examples. It's a known fact: In the 1990s, the US government recruited eminent game theorists to address strategic issues. In particular, Professor Robert Aumann was a consultant to the US Agency for Arms Control and Disarmament. This was the period when the USSR collapsed and there was a serious problem of the potential uncontrolled "spread" of nuclear weapons and no one was interested in that. At that time, our country was conducting intensive negotiations with the United States. The parties tried to conduct a dialogue and find a joint solution to the problem, which ended with the signing of a number of serious international agreements on strategic arms control.

  

You have already mentioned that you set the conference the task of attracting the attention of the business community. Are business people interested in game theory?

Today, constant close interaction with business is the main issue in the application of game theory in management. Business is well aware of management problems, but often requires urgent advice on how to solve it. If the problem is serious, then this approach does not fundamentally cope with it, often only external manifestations are visible. The involvement of specialists requires resources and a certain amount of time associated with the study of the problem, its mathematical and quantitative modeling, verification of the adequacy of the apparatus used. But, unfortunately, business circles often do not have such a request — it is “too long” and sometimes costly. Although it actually leads to business losses, especially when we look at long periods.

Therefore, we need joint continuous work, perhaps in particularly important and difficult areas. We do not ask business to formulate the problem mathematically — let there be at least specific cases for a start, and academic specialists can formalize the problem. A specific verbal description of the problem, a verbal formulation of the problem — this can only be done with practice. And the matter does not end even with finding a solution to the developed model. What if it doesn't suit the business? Maybe the constructed model was, for example, too simple and did not take into account all the specifics of the real situation? Then it will be necessary to continue work on creating a more complex model adequate to the problem under study.

The process of interaction between applied mathematicians and business should be constant and long-term, in our case it concerns the study of conflicts. You need to support teams, long-term research, so that interdisciplinary and competent teams can focus on solving business-critical problems, then there will be breakthroughs.

  

Can you give examples where game theory would help solve understandable problems?

Lloyd Shapley and Alvin Roth received the Nobel Prize for their work that dealt with "the application of economics — how to design specific markets so that they work well." In particular, one of the results obtained by Shapley is the so-called Shapley-Gale algorithm.

The well-known interpretation of the problem is as follows. There is a subset of women. They all want to find a husband. And there is a subset of men who want to find a wife. Each participant has their own priorities for choosing a partner. Which pairs should form? At the same time, it is required that in each new pair both are satisfied: both the man and the woman. So the Shapley-Gale algorithm helps to cope with this task. With this decision, not necessarily every applicant will find a match for himself. But the members of formed couples will be happy.

There is a more vital application of this algorithm. It is known that there are donors who donate their organs. And there are recipients who need them. Obviously, there are many compatibility criteria here. Which organs to supply to whom? This very serious and specific problem is also being analized by this approach.

Or another example, building a car route in a city, taking into account traffic congestion. You have a navigator that builds a route. In practice, it is not always optimal in terms of travel time. This problem has recently been solved based on game theory. When building a route, it is taken into account that other road users are optimizing their route. As a result, a new algorithm was developed, adjusted for the behavior of road users, and not only for distance, congestion and information about traffic jams.

  

Will there ever be a day when game theory will form the basis of algorithms that will serve for developing mobile applications for business? Will they be able, using these tools, to simulate the development of situations and make operational business decisions online?

I'll start with a story. I got my start in game theory when I was at university in the 1970s. In the lectures, one of the basic models was the game of chess. What is the game of chess in terms of game theory? It is a sequential, antagonistic, dynamic game with complete information. The state of the game is determined by the position of the pieces on the board, which is known to both players. According to the rules, White makes the first move, Black makes the next, etc. It is interesting that from the point of view of game theory there are no special problems. This game belongs to the class of multi-step games with complete information, and for such games there is always an equilibrium in pure strategies. This means that theoretically, there are optimal strategies for both players. In other words, if the players stick to these strategies, the result will be a predictable result: White wins, Black wins, or there is a draw. However, due to the large dimension of the problem, no one has yet been able to calculate these optimal strategies.

Then computers appeared, and grandmasters began to play chess with them. At first, serious chess players won almost all games against a computer. On a rare occasion, the machine would beat the grandmaster and it was such an event that he was reported in the press. Now, on the contrary, it is a serious event when a grandmaster plays chess with a modern computer and wins.

Even during my studies at the university, we knew that games like chess, checkers and other sequential games with complete information about the position (as opposed to cards, where there is no balance in pure strategies) are games with a time-limited lifespan. Sooner or later it will be possible to play chess without even knowing how to do it. All the necessary moves will be prompted by the program in your mobile phone, and you will simply follow the algorithm and move the pieces.

  

Obviously, in the 70s, you could not imagine such a situation even in your wildest fantasies ...

And until recently, we could not imagine mobile phones or a computer that would fit in a pocket. We could not imagine the possibility of processing huge amounts of data and, most importantly, that completely different approaches to this very processing would appear.

Therefore, I think that sooner or later this will happen: businessmen will use special mobile applications to choose the best solution in a specific conflict situation. And in order to find the optimal algorithm, they will press a button, as when choosing moves during a game of chess. But this is not always applicable. The manager will have ready-made solutions for most typical situations. However, there will be new challenges, new conflicts that will require new solutions, and mathematicians will offer new tools to find them. The intellectual work itself will become more instrumental and maybe very smart people will have more time to think about their reputation, the moral component of their activities, the historical past and future, relationships between people.

It is important that in any historical perspective, you still have to think.

    

Each conference "Game Theory and Management" is illustrated with a masterpiece of world art. You put it on a poster, on the cover of a collection of publications. How did this tradition come about?

Somewhere in the early 2000s, Leon Petrosyan and I traveled a lot to international conferences, delivering research reports. During this period, we gained a lot of experience in organizing such conferences, knew the organizer, talked a lot with them and consulted. It was then that we had the idea to create our own annual international conference on game theory and its applications in management at St. Petersburg University, which would meet the highest international standards.

It should be noted that Leon Petrosyan is a great connoisseur and lover of art, and knows painting very well. On those trips, he and I constantly went to museums, where he constantly drew my attention to paintings with game plots. As a result, there was an idea to raise "to the title" of our future conferences' works of art with game plots. At the very start, we even picked up a bank of paintings, within 10 pieces. Of course, it ended long ago, but we are constantly replenishing our basic collection. This year, at the title of the XV International Conference "Game Theory and Management", the painting "Vabank, or Gambling" by the artist Eduard Svoboda, 1849 (The name in German is "Gluckspiel").