Game theory and cryptocurrency

Game theory is one of the branches of applied mathematics that studies the optimal strategies of action in different “game” situations. It allowed developing the basic principle of the organisation of decentralised cryptocurrency networks. And it ensures their safety, too. However, its application is not limited to this — economics, geopolitics, sociology, psychology and even zoology — game theory has found its application in all these fields of science.

Case study

Game theory usually operates with models — “game situations” that demonstrate examples of rational behaviour and tactics of developing the optimal line of behaviour. The Prisoner Dilemma is used as one of the most frequent examples.

The situation is as follows. There are two criminals. Both have been interrogated, and they could not agree in advance about their actions. If both are silent, then they will be imprisoned for a year due to lack of evidence. If both hand over an accomplice, then each will be imprisoned for 2 years. And if one is silent, and another confesses, then the silent person will be imprisoned for 3 years, and the “talker” will be released. What is the best strategy in this situation?

It is understood that both people are able to reason, calculate other people’s behaviour and think logically. A small but admissible convention of game theory. So, liberation is, of course, the best result. However, each of the participants understands this, so the first “impulse” is to blame everything on the accomplice. Plus, this is precisely what “irrational behaviour” is — the fear of punishment and a tendency to deny everything in the hope that “danger will go away”. As a result, 2 years for each. Not at all what was originally calculated. Therefore, it is worth considering that “you are not the only one so smart” and acting, taking into account the possible interests and actions of another person. It is called “rational behaviour”, which claims that it is worth relying on the accomplice’s rational thinking to get everyone just a year of conviction.

However, as shown by “investigative experiments”, rational behaviour is quite a rare phenomenon in such situations. That is why game theory is not a universal way to make decisions.

However, there are several basic points that must be observed in order for game theory to work at all.

• Multiple members
• Uncertainty of behaviour (participants can choose different strategies)
• Different goals and interests of participants
• Interconnection (the actions of one person affect the others as well)
• Clear rules that everyone knows.

It follows that in situations when players are not equal, when someone has no idea about the game rules, when one of the players has no choice and when somebody cannot act rationally, the game theory does not work. It could be said that it describes the interaction of the governments of different countries but not the government and the people.

As for cryptoeconomics, it fully meets all the necessary requirements. Individual participants are equal to each other, clearly know the rules of interaction, pursue personal interests and are forced to interact with each other. Let’s consider this situation in more detail.

Game theory and cryptocurrency

So, there is a peer-to-peer system with a bunch of nodes endowed with the same authority. There are clearly defined rules for interaction, which is also rewarded. But there is freedom of choice — each individual node can choose whether it follows the rules or not. From a technical point of view, forging information in a blockchain block is real. But in order to distribute it to the entire network ahead of new blocks constantly “building up”, you need a lot of resources. Much more than can be obtained through such fraud. And the punishment for nodes seen in fraudulent schemes is immediate and strict. Therefore, a rational behaviour strategy in this situation is to act within the system frameworks, honestly mine and confirm the receipt of new blocks. However, in small systems with a small number of nodes, the chance to “take control” still exists.

The blockchain structure itself forces users to follow its rules. Yes, there will always be those who try to get what they want in a fraudulent way. However, false data from individual nodes does not affect the integrity and performance of the entire system. This is called Byzantine fault tolerance (BFT), or the “Byzantine generals problem”.

Conclusion

If it were not for game theory, it would be impossible to create a system that encourages users to act both rationally and within the rules. However, the theory alone was not enough — it was still necessary to somehow protect information at different levels. Exactly for this purpose, quite sophisticated confirmation mechanisms were introduced: Proof of Work and Proof of Stake. They were needed as both restrictive factors and possible punishment.

Nowadays, game theory is used not only to create new blockchains but also to calculate the dynamics of cryptocurrency exchanges. With varied success, however, since human behaviour, even in the economic aspect, is far from always rational.