Game theory is a science on the border of mathematics and economics.



The theory of games itself originated with economic theory about three centuries ago, but it was John Forbes Nash who turned it into science, no, it is not related to Forbes magazine.



Nash’s biography is well known, but his work is still a mystery to many. Today I will try to begin to reveal the essence of game theory and start from scratch.



Strategy game



“Game” - hearing this word, many people think that it is a question of something insignificant and not large-scale, especially in comparison with the world economy, business or military affairs. In fact, strategic games include not only military and business strategies, but also economics, career building and relationships, and much more. Almost everything that surrounds us belongs to strategic games, and game theory helps in all this to understand.



But enough of the lyrics, everyone already understood that strategic games and game theory are the most important things that can happen in life, which means that it’s time to start analyzing examples.

Round stroke

Tennis is a great field for strategy games. What should Player A do in order to beat Player B - to hit the field line or diagonally? Should player A expect to hit the line and tilt in one direction or count on a diagonal strike and lean in the opposite direction?







The most effective is a blow to the line, here the ball will fly less, and the enemy will have less time to react. But if you constantly use it, the game will be too predictable, which means the enemy will be constantly ready to strike. Consequently, it is necessary to use a blow on the diagonal quite often, and then player A will have to make a decision every time either in favor of counteracting a strike on the line or on the diagonal.



The main principle of action in this situation:



Player B should focus on what is better for him not to do than on what should be done. Otherwise, player A will be ready to strike and the chances of success will be lower.



This example well illustrates the situation in the film, where the main character needs to poison one of the glasses and offer it to the villain, but where is the guarantee that the villain does not guess the hero's intentions and does not take the glass with un-poisoned wine, especially if he had already encountered something like that.







Conclusion: in similar situations one should act haphazardly, and it is better to poison both glasses, then this will definitely work. But do not forget about the antidote!

Rat race

The dilemma of prisoners has been known for a long time, but how to apply it in other cases than the inquiry.



Imagine that you enrolled in a course where grades are based on average performance. At the same time, regardless of your success, only 40% of students will receive an “excellent” mark, while the other 40% will be “good”, for the remaining 20% ​​these grades will be unavailable, no matter how good their results are in absolute terms.







It turns out that to achieve good results you need to work not only in learning as such, but also to monitor the success of your comrades. Most of the students understand that this is all mouse scuffling, and after the first lecture they are going to agree not to show excessive zeal in their studies.



And everything would be fine, but after a couple of weeks, the desire to get good grades becomes too strong, and students begin to break the agreement, spending more and more time studying. In addition, your fellow students do not know about the volume of your efforts and cannot somehow influence you, and the high score is clearly worth a little more effort.



But the problem is that the rest of the students do the same, and as a result, you will receive exactly the same grade, as if everyone adhered to the agreement. There is only one difference - you will spend more time on study than you would like.



It is considered that in any game there is a winner and a loser, but the prisoners' dilemma is not one of them - all players can lose in it as well as win.



Prisoners' dilemmas include a variety of daily activities, such as an arms race or when you get up from the stadium for a better overview. All cases are different, but they are united by one thing - since all participants follow the same path, the result remains the same, and none of the participants of the game gets a significant advantage.

Flat tire

In America, among students there is a common bike, well illustrating the strategy in games with successive moves. The situation is similar to the prisoners' dilemma, but still a bit different:



Two students studied chemistry, tests and laboratory tests were well passed, and only the exam remained for final certification. He was scheduled for Monday, and the guys were determined to receive the highest rating, but it turned out that on Saturday they decided to relax at a party. As a result - all Sunday instead of preparation, they lain with a hangover.



Understanding that without preparation, they had little chance of passing the exam perfectly, the students decided to tell the chemistry professor a touching story about a flat tire, because of which all the weekends were for nothing, and they could not get ready. They also asked to take their exam tomorrow, as they had just arrived and were very tired.



Thinking, the professor agreed, and the guys went to urgently study the materials.



When they came to the exam the next day, they sat down for different audiences and were given a task. The task consisted of only two questions: the first was very simple and was rated at 10 points on a 100-point scale, and the second was on another page and was rated at 90 points.



The second question was a simple phrase: “So what kind of tire did it lower?”.



This excellent story has two important strategic lessons: do not underestimate your opponent and you should figure out future moves in advance, and then analyze them in reverse order to determine the optimal actions.



By the way, due to the fact that the students did not agree in advance on the answers, the probability of their coincidence is only 25%.



For the correct answer, you need to think not only about the logical and obvious answer, but also about its obviousness to a friend. Thus, one can guess to infinity. And although a logical answer seems to be the front right wheel because of its proximity to the side of the road, where glass and nails can be, but when interviewing students over 50% answered the front left. Why - no one knows, but this answer seemed more obvious to them.

Protection against manipulation

Many teachers do not tolerate exams under any circumstances. On the one hand, this may seem cruel, but if you think about it, their position becomes clear.



Most teachers are kind and responsive people, and they would be happy to give students a break, but because of their kindness they can get into a difficult situation.



Feeling weak, students can start using it and, as a result, the learning process can be thwarted, because it is not always possible to distinguish truth from lies, especially if the excuses are of the same type. So you have to take everything on faith.



The easiest way to avoid embarrassing situations and future inconveniences is not even to start giving any indulgences. But how to make your failure reliable. The best way is to refer to the administration of the institution and its instructions, because if it does not follow them, the teacher can be punished.



But what to do if the administration does not give life-saving restrictions - in this case, you should refer to your own principles and voice them when meeting with students. And as soon as the situation with excuses arises, recall the principles voiced and call for a sense of justice: "If I go to concessions with you, you will also have to do with other students, and you know - this is unacceptable."



This strategy has commitments and associated promises and threats. An extensive topic on which to build many other game strategies.

Pull to the last

Many have experience of living in a dormitory or in a rented apartment together with friends, and probably in the process of accumulating this experience there were situations when the powder or detergent runs out, but there is no desire to follow them. Then we begin to hope that the neighbor comes down and buys, and we pull to the last, or will we go to the store and get the necessary things? It happens in different ways, but often everything is dragged down to the last, and it is the one who is “lucky” to encounter the finished, but very necessary laundry detergent or something else that goes to the store. Such situations happen to come to conflicts and large quarrels, but we will consider it from the side of a strategic game.



The situation should be considered from two sides.



The first is a simple binary choice - go or not go to the store. And here is the best option - if the neighbor goes to the store, and you stay at home, and the worst - if you go, and the neighbor will sit in front of the console. At the same time, if both of you go to the store without informing each other, then unnecessary duplication of purchases and possible food spoilage will occur, and if no one goes, then a local catastrophe is possible, such as, for example, finished toilet paper, about which someone can find out in the hour of need. One of the names of this strategic game is the game of the coward.



The second is the war of attrition, and it is somewhat more interesting. In this war, each participant tries to wait out the neighbors and expects that someone will end the patience earlier. At the same time, the risk that something important will end and a catastrophe will occur and the ensuing quarrel will increase. Here, each player admits the aggravation of the situation to his point of tolerance, and in the end loses the most impatient. In this war, each participant evaluates the willingness of other players to reach a catastrophe, and this is called "balancing on the edge." This is also a variation of the game in a coward, but more dynamic.



Edge Balancing is a game with increasing mutual risk, and it can have only two outcomes. The first is that one of the players reaches his point of tolerance and is inferior, and the second is the risk rises to a critical level and a quarrel arises. Most often the second option is much worse for everyone.

Date game

When you gather for a date, you want to appear in front of your partner in the best possible way and make the best impression on him, because if you do not succeed, then the relationship may not come out - there will not be a second chance to make the first impression.



At the same time, you would like to know not only about the positive features of your partner, but also about the negative ones - you want to be ready for everything. But the snag is that not only do you know the art of dating.



So it turns out that during the first date, both you and your opponent will evaluate each other, trying to understand what negative qualities you are hiding from each other, and that of the positive ones shown is true and not false. For example, gifts can show generosity and willingness to sacrifice something for you, but gifts should be evaluated in terms of value for the opponent. A bouquet of flowers for a student will be as valuable as a diamond ring for a billionaire. But the time of the billionaire can cost much more than the ring itself.



In addition, the filing and concealment of information occur not only on the first date, but throughout the relationship. Here is a story that perfectly illustrates this:



In New York, a man and a woman rent apartments with state-regulated rent. Such housing is always beneficial to rent, unlike private offers. Relationships of the couple developed, and they came to the decision to live together. The woman offered to live with her and refuse the man from his apartment. But he decided to leave the apartment, explaining that it is always better to have several options. And since the probability of a gap, although minimal, remains, it is better for him, considering the risk, to leave the rental apartment profitable for rent. The woman took the answer negatively and broke off the relationship.



Rationalists confirm the expediency of a wide choice, but in this case the reason for explaining the actions of a woman should be considered from the side of strategy. Since she was not sure of her partner, she decided to check his reliability in this way, and he did not pass this test. It is not enough to say “I love you”, words should be confirmed by deed, and in this case, the confirmation would be a break in the lease agreement, and the man’s refusal would be sufficient confirmation of the opposite. And the gap between women was logical.



This example belongs to the class of strategy games, based on their own experience, and their main tool is information manipulation. So the strategies that convey information are called signals, and the strategies that encourage disclosure are screening tools. Similarly, in the example, the actions of the woman were screened, and the actions of the man were a signal. The methodology for using screening and signaling strategies is wide and worthy of a separate publication.



On this, perhaps, finish. As always, I will be happy to add and discuss in the comments.

Have a nice day, everyone!

---

Literature:



“Strategic games. Available textbook on game theory

Authors: Dixit Avinash, Skit Susan, Railey Jr. David

Mann, Ivanov and Ferber, 2017

ISBN: 978-5-00100-813-2