Professor Auzin’s science column
Marcis Auzins: “Why read my texts? It seems to me that we often tend to “ignore” natural sciences, saying that they are formal, dry and uninteresting. I would like to let the reader see that they are a part of our lives – colorful and interesting.”
Biography punctuation marks:
- A physicist by profession, currently a professor at the University of Latvia, head of the Department of Experimental Physics and the Laser Center.
- From 2007 to 2015, he was the rector of the University of Latvia.
- Works in the field of quantum physics and is the author of more than a hundred scientific articles published in the world’s leading physics journals and several hundred conference reports.
- Together with colleagues from Riga and Berkeley, he wrote two monographs, published by “Cambridge University Press” and “Oxford University Press”, both of which have been reprinted.
- During his career, he lived and worked in different countries – China and Taiwan, the United States, Canada, England, Israel and Germany.
For example, you can offer one euro to a colleague and keep ninety-nine for yourself. It might seem that the colleague does not gain much, but still more than nothing. So why not accept this offer? However, other human factors, such as a sense of justice or wrongdoing, also envy, come into play here in addition to pragmatic considerations. This is an artificially constructed situation, but it is easy to imagine parallels in life. Is the salary offered by the employer fair? In other words, doesn’t the businessman keep too much for himself? Does the bank not charge too much interest for the loan, wanting to make money at my expense, and many similar situations.
Sometimes you just want to imagine that business is only about how to offer a cheaper and better product or service, thus “cutting the buttons” of competitors. However, many additional aspects and human relations often play a role in business as well. It is conceivable that the owners of one business, for some personal reason, do not humanly see the owner of a competing business. Then a situation may arise that not only economic aspects play a role in competition. It can happen that the hatred is so great that there is a motivation to destroy the competitor, even if one’s own business suffers or dies in the process. The described and similar situations are studied by a branch of mathematics called game theory.
Perhaps some of the readers still remember the 2001 feature film “A Wonderful Mind”, which depicted the life story of a real person, the American mathematician John Nash. In this movie, Nash is played by American actor Russell Crowe. In real life, mathematician John Nash was awarded the Nobel Prize in Economics in 1994 along with his fellow economists Reinhardt Zelten and John Harsanyi. They received it for a branch of mathematics with an intriguing name game theory and developing its applications in the economy. John Nash was born in the United States in 1928. John developed his main ideas while still a doctoral student at Princeton University. However, in the late 1950s, he developed serious mental health problems and was forced to spend several years in a psychiatric hospital. However, as his health improved, he managed to return to academic work in the 1980s, both in research and teaching students. The film about Nash generated no less interest than the recent film about the physicist Robert Oppenheimer. Outstanding personalities always fascinate.
And yet. What exactly is game theory and why is it of interest not only to mathematicians, but also to biologists, economists and even researchers in political science? As the name suggests, it is a theory that studies various games in which players make decisions to achieve the best possible outcome by cooperating or not cooperating in a strategic competition. So to speak, the task is to get the best possible score in the game.
The first thing that comes to mind when thinking about games is, for example, chess or the insole so beloved by Latvians. But it turns out that with the concept the game one can understand a much wider range of life situations – both in economics and biology and also in politics and international relations, where both rational considerations and human emotions play a large role.
Another example often used to illustrate game theory is the so-called Prisoner’s Problem. Imagine this situation. Two people have committed a crime together. They are detained and kept in separate cells, without the possibility of communication. However, there are no witnesses to the crime and the only possibility to punish them is their confession. The rules are as follows. If none of the detainees confesses, then after the investigation, which will last about a month, they will be released due to lack of evidence. If one of the detainees confesses and the other does not, then the one who confesses is immediately released, while the other must spend 12 months in prison. However, if both detainees confess, each of them will be imprisoned for six months. What to do?
The best option for both prisoners would be not to confess and be released after a month. However, human bad nature can play a role here – one of them might want to “leave” at the expense of the other. To confess, hoping that the other person will not confess. However, if the other detainee also wants to use this tactic, then both will be imprisoned for six months. People would call it a psychological game to make a decision without knowing how the other person will act.
One solution to this game is as follows. It is necessary to act in such a way that the situation of the decision maker is the best possible, regardless of the decision of the other player. So it must be confessed. Then the player will be released no later than after six months. If you don’t confess, there is an option in the event of a certain course of events – the accomplice confesses – to be imprisoned for twelve months. This strategy of getting the best outcome regardless of other players’ decisions is called a Nash equilibrium. In the prisoners’ problem, the Nash equilibrium occurs when both prisoners confess. This balance represents the eternal search for a balance between personal and collective good.
By the way, the search for this balance is vividly manifested in real life, for example, in international relations and armament policy in the modern world.
It would be best for everyone if countries did not arm or, even better, disarm. However, if one disarms and the other accumulates weapons, the situation is dangerous. Therefore, whether we like it or not, the amount of armament and its destructive power in the world is not decreasing.
Another interesting element of game theory appears here. There are games where players have opportunities to talk and agree with each other, and games where these opportunities are not available. If there are agreements, such as international treaties, then the question arises as to what mechanisms are in place to ensure that they are respected. This example brings together all the opportunities, challenges, problems and action strategies of today’s world, as well as tactical solutions to keep in mind.
Humanity has faced such and similar decision-making since its inception. For example, historians tend to quote the first century AD Roman senator Pliny. He describes a situation that lends itself well to game theory analysis. The Roman senate had to vote on the fate of a group of citizens accused of sedition. Three very different versions of the verdict have been discussed. Acquit the group, expel the accused from Rome or the third option – sentence them to death. The smaller group of senators, to which Senator Pliny also belonged, is said to have advocated an exculpatory decision. The majority of senators were said to be in favor of the death penalty.
If each senator voted according to his conviction, the majority would be in favor of the death sentence. However, Pliny urged his associates to vote tactically. It meant voting for deportation. This did not seem like the best decision to the group to which Pliny belonged, but by voting in this way with the other group of senators, it was possible to avoid the death sentence. This situation is well described by game theory.
The examples mentioned may seem simple, even primitive. The question arises, where is the mathematics and for what Nash and his colleagues were awarded the Nobel Prize?
The situation becomes much more complicated when the number of players increases and their interests differ significantly. Then, finding the best solutions requires serious modern mathematical theory. Game theory in the modern sense was developed in the middle of the 20th century by one of the outstanding mathematicians of Hungarian origin, John von Neumann. He is rightly considered a genius. He started studying at the University of Budapest at the age of 15 and received his doctorate in mathematics before he was 20 years old. He is perhaps more often remembered for developing the mathematical foundations of quantum physics, but Neumann began his career in mathematics directly by proving several very important theorems in game theory. Much more could be said about John von Neumann and his time in Hungarian intellectual history. The fact that a relatively small country like Hungary produced so many outstanding scientists and artists in the 20th century (in addition to von Neumann, one could mention the physicist Leo Szilard, the creator of holography Denis Gabor, the composer Biel Bartok, as well as the writer and Nobel laureate Imri Kertész ), gives rise to a lot of thought.
So much (actually, so little) about game theory. If what you’ve read has piqued your interest and game theory seems worth further study, I can recommend the free introductory course in game theory available on the online learning platform “Coursera.org”. (Game Theory I) offered by Stanford University in the United States. However, it should be taken into account that this will be a real learning course, which requires time and effort to learn.
Professor Auzin’s science column
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2024-01-19 05:31:39
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