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Game theory is the platform for the growth of cryptocurrencies and is one of the reasons why Bitcoin can thrive for more than a decade, despite countless attempts to disrupt the Bitcoin network.

## What Is Game Theory?

Game Theory is a method to approach to understand and analyze the behaviors or decisions of each individual and group of individuals in a contradictory situation. It pursues two basic assumptions are mathematics and economics. First, it assumes each individual or group of individuals is a participant in a game and their goal is how to gain benefits (be it winning or reducing the damage). Second, it considers every human action to be guided by the principle of sufficient reason in the sense that before each decision, the individual tries to calculate his/her own benefit/damage when making a decision.

Particularly, Game Theory is an applied mathematical method used to study human behavior based on rational decision making. The “game” is designed as an interactive environment, so players tend to take reasonable action in response to game rules or effects from other players.

Originally, Game Theory was developed in economics to study the behavior of businesses, markets, and consumers, it is now widely used in other areas of research. Therefore, its models can be used as a tool to examine the potential behavior of interacting agents and possible outcomes from their actions in predefined cases. They can also be applied in extensive research on politics, sociology, psychology, and philosophy.

## Prisoner’s dilemma

The game “Prisoner’s dilemma” can be summarized as follows: Suppose the police catch two suspects for storing small amounts of drugs, with a possible sentence of one year in prison. The police have reason to believe that both of them are real drug dealers, but there is not enough evidence to accuse them. If they were proven to be true drug dealers, they could face up to 25 years in prison. The police know that one man’s testimony against the other is enough to convict the other convict of drug trafficking. So he/she said they would acquit either of them if they provided evidence that the other person was guilty of drug trafficking. In case both provide evidence against each other, they both receive the same sentence of 10 years in prison. The police put forward this plan because they want to detain both for 10 years, otherwise, two offenders will be imprisoned for only one year and will quickly leave prison to continue their crime.

Both suspects were locked in separate cells and not in contact. Each of them has the same dilemma: if he denounces the other, the other will have to spend 25 years in prison and he will be free, or not denounce and keep silent, he will be imprisoned for a year. But if both denounce each other, they will have to serve 10 years in prison. Each of them might think, “It’s better to report it. If that guy didn’t accuse me and kept silence, then both would be in prison for a year. But what if that guy denounced? In that case, if I made a confession, then I would have to go to jail for 10 years, but if I stayed silent, then that guy would be free and I would be sentenced for 25 years. Would that guy not accuse me, If I helped him by staying silent?”

This is a typical example of the dilemma caused by rationalistic independent acts. The best solution for one side is denouncing the other and being free. The second-best result is both of them stay silent and take one year in prison. The worse result is that they both denounce each other and then received a 10-year sentence. But the worst ending is still stabbed in the back in the case of keeping silent while the other denounced, and then the silent keeper has to serve 25 years in prison. Choosing the best option, ie freedom, is synonymous with a rational choice, but if both unilaterally choose the best option for themselves, both must suffer the same bad ending. Without communication, cooperation becomes difficult. If they had talked to each other, both of them could have agreed to keep silent and would have been imprisoned for only one year.

However, even when it is possible to communicate with each other, there are still problems that are not easy to solve, trust and reliability. In the Prisoner’s Dilemma, each suspect may tell himself, “We are all drug dealers. I have seen his style of doing business. After agreeing to be silent, how do I know if he was traitor and said, “Ah, I convinced him to keep silent? Now I will choose the best solution for me to not be imprisoned.”

## Game Theory and Cryptocurrencies

When applied to Cryptocurrencies, Game Theory models play an important role when designing a secure and no-trust economic system, such as Bitcoin. The creation of Bitcoin as a Byzantine Fault (BFT) system is the result of a harmonious combination of cryptography and Game Theory.

The use of Game Theory in the context of Cryptocurrencies gave birth to the concept of Cryptoeconomics. Basically, it is the study of the economics of blockchain protocols and the potential consequences that the design of these protocols can bring – as a result of the participant behaviors. It is also considered “outside factors” that are not actually part of the ecosystem but can participate in the network for the purpose of causing disruption from within.

In other words, Cryptoeconomics studies the behavior of network nodes based on the incentives provided by the protocol, analyzing the most reasonable and most probable decisions.

Because the Bitcoin blockchain is designed as a distributed system, many nodes are scattered in different locations, so the authentication of transactions and blocks needs to rely on the consensus of these nodes. However, these buttons can not really trust each other. So how could such a system avoid harmful activities? How can a blockchain prevent being broken by dishonest nodes?

One of the most important features of the Bitcoin network that helps protect it from harmful activities is the Proof of Work consensus algorithm. This algorithm applies encryption techniques that make the digging process very wasting and complex, creating a highly competitive mining environment. Consequently, the structure of PoW-based cryptocurrencies encourages mining nodes to operate honestly (nodes will not risk losing resources invested). In contrast, any harmful activity is discouraged and quickly punished. The act of dishonest mining can cost a lot of money and will be removed from the network. Therefore, the most logical and most likely decision from a miner is to act honestly and keep the blockchain secure.

## Conclusion

The common application of Game Theory is to model and test how people behave and make decisions based on rational deliberation. Therefore, Game Theory models must always be considered when designing distributed systems, such as Cryptocurrency systems.

Thanks to a well-balanced combination of Cryptography and Game Theory, the Proof of Work consensus algorithm was able to create the Bitcoin blockchain as a decentralized economic system and highly resistant ability to cyber attacks. This is the same as other cryptocurrencies, and the concept of Game Theory also applies to PoS-based blockchains. The main difference here is how a Proof of Stake blockchain handles transactions and proceeds with block validation.

However, keep in mind that the level of blockchain security and resilience depends on its protocol and is directly related to the number of participants in the network. Large distributed networks are more reliable than small distributed networks.

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