Translated with AI
Game theory concepts are used in a variety of fields, from advanced poker rules to stock trading. We discuss several common dilemmas related to rational risk assessment.
The El Farol Dilemma
The game's premise: every Friday, El Farol Bar puts on a new entertainment show. Every week, regulars are faced with a choice: whether to go to the bar that evening or not. For simplicity's sake, let's assume there are only 100 of them. The problem is that the bar itself isn't very large. If 60% of the patrons go in, they'll have a less enjoyable time than if they stayed home. However, if up to 60% of the regulars are in, the opposite applies.
So, everyone has to try to guess how many customers will show up at the bar on Friday. If they think the place will be crowded, they skip the evening. If they think the crowd will be small, they head to the bar.
The essence of the dilemma is that this decision must be made independently, without regard for others, and based solely on the number of patrons at the bar last Friday. The bottom line: even if every regular has a reliable strategy, if they all use it simultaneously, they will lose. El Farol's problem has become the hallmark of the game of minority shareholders, where the minority always loses.
Prisoner's dilemma
Two criminals, A and B, were caught simultaneously committing similar crimes. Police believe they conspired and offered identical deals.
If one testifies against the other, and the other remains silent, the first will be released for cooperating with the investigation, while the other will be sent to prison for 10 years. If both remain silent, each will receive six months. If both testify, the sentence increases to two years.
Both must choose: remain silent or testify. The criminals don't know what the other will do. What will happen?
The dilemma can be broken down into a table :
| B is silent | B testifies | |
| But he remains silent | Both are jailed for six months. | B is released, A gets 10 years |
| And it testifies | A is released, B gets 10 years | Both are sentenced to two years in prison. |
The problem arises when both criminals care only about their own freedom. How can one reason: if the accomplice remains silent, it's better to testify against him and go free. Otherwise, six months in prison.
If he testifies, it's worth doing the same to get two years in prison instead of ten. The "testify" strategy is far superior to "silence." Similarly, the second criminal reasons in the same way.
Deer hunting
During a deer hunt, everyone understood that they had to maintain their post. But if a hare ran past one of the hunters, there was no doubt he would chase it and, having caught the prey, care little about how his actions deprived his comrades of their catch. The dilemma reflects the conflict between personal and social interests.
Battle of the Sexes
A married couple must choose where to go this evening: a football match or a romantic play. Participants are not allowed to communicate or cooperate; decisions must be based solely on their own desires or anticipation of the other's actions.
The husband will receive a benefit of two points if he and his wife go to a football match and one point if they go to a play. The wife's benefit works in the opposite direction: two points for the play and one for going to the stadium. If they each go where they originally intended, they will each receive zero points, since they prefer to spend time together rather than alone.
If a husband is confident his wife will choose the play, he'd be better off going with her than going to the match alone. If he thinks she'll go to the football game with him, he shouldn't give up on his original intention. The wife's reasoning will be similar.
Ultimatum
Two people participate. The first receives a certain amount of money. They must split it with the second in any proportion. The second can either accept the proposed amount or refuse, in which case both lose the money. The rules of the game are set in advance.
No matter how much money the first player offers, it's always advantageous for the second player to accept, since otherwise both will end up with nothing. It's reasonable for the first player to increase the amount. These statements only work if both players act rationally. But in reality, on average, during experiments, the second player is offered 30-40%. However, if less than 20% is offered, it's usually rejected.
