How Does Game Theory Apply to Crypto?

Despite numerous attempts to disrupt the network, Bitcoin has thrived for over a decade. Game theory played a fundamental role in the development of cryptocurrencies, contributing to their success.

Basics

Game theory is a method of applied mathematics used to study rational decision-making in human behavior. The interactive game environment encourages players to act rationally when responding to the rules or the influence of others. Originally developed in economics to study business, markets, and consumers, it is now widely used in other fields of study. Game theory models can be used to examine the behavior of interacting agents and the potential outcomes of their actions under predefined circumstances. This approach can also be applied in the study of politics, sociology, psychology, and philosophy.

The Prisoner's Dilemma

Considered a classic game theory model, the prisoner's dilemma illustrates a scenario where two criminals, A and B, are being interrogated separately after being arrested, unable to communicate. The prosecutor aims to persuade each criminal to testify against the other to reduce their charges. If A testifies against B, A is released, and B is sentenced to three years (and vice versa). If both betray and testify against each other, they are sentenced to two years each. If both stay quiet and do not betray, they are sentenced to one year only due to insufficient evidence.

From this, we get the following results in the form of a table:

Optimizing individual self-interest in the Prisoner's Dilemma would result in betraying the other person to be set free, but the uncertainty of the other's decision makes it an unpredictable strategy. Most rational prisoners would choose to betray, considering the reward offered. However, if both A and B betray, they will be jailed for 2 years, which is not the ideal outcome. Therefore, the optimal decision for both prisoners as a pair would be to remain silent, resulting in a sentence of only 1 year in prison. This simple scenario exemplifies the use of game theory models in understanding human behavior and potential outcomes based on rational decision-making.

Game Theory in Crypto

Game theory models play a crucial role in designing secure and trustless economic systems for cryptocurrencies, including Bitcoin. The creation of Bitcoin as a Byzantine fault-tolerant (BFT) system is a successful fusion of cryptography and game theory. This combination has led to the concept of crypto economics, which explores the economics of blockchain protocols and the potential impacts of their design on participant behavior. Crypto economics also considers the behavior of external agents that could attempt to disrupt the network. In short, crypto economics studies the rational and probable decisions of network nodes based on incentives provided by the protocol.

Proof of Work Solution

To ensure trust in the Bitcoin blockchain, it relies on the agreement of distributed nodes to validate transactions and blocks. However, since these nodes cannot trust each other, the network requires protection from malicious activity. One key feature that addresses this issue is the Proof of Work consensus algorithm used by Bitcoin. By making the mining process demanding and competitive, the PoW architecture incentivizes mining nodes to act honestly, as dishonest behavior risks losing invested resources and being expelled from the network. As a result, the most rational decision for miners is to maintain network security by acting honestly, while malicious activity is discouraged and punished.

Conclusion

Designing distributed systems like cryptocurrencies requires taking into account how people behave and make decisions based on their rational minds, which is the main application of game theory. The Proof of Work consensus algorithm was created by combining cryptography and game theory to develop the Bitcoin blockchain, a decentralized economic system resistant to attacks. The security and resilience of a blockchain depend on its protocol and the number of network participants. Larger distributed networks are more reliable than smaller ones.