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The game theory of Bitcoin and cryptocurrencies

The game theory of Bitcoin and cryptocurrencies

The characteristics unique to cryptocurrencies make them an intriguing topic for analysis in game theory, as they can help to explain the behaviors and incentives involved in trading and investing. This article delves into the concepts of mining cryptocurrencies, the prisoner’s dilemma, and blockchain forks that are relevant to the game theory of cryptocurrencies and Bitcoin.

Introduction to game theory and cryptocurrencies

Game theory is a mathematical framework that provides an explanation for decision-making in strategic situations. Cryptocurrencies, like Bitcoin (BTC), have become a popular subject for game theorists due to their decentralized nature and their potential to disrupt traditional financial systems.

The prisoner’s dilemma and cryptocurrency mining

In the classic game theory scenario known as the prisoner’s dilemma, two parties must make a choice without knowing what the other will do. In the context of cryptocurrency mining, the prisoner’s dilemma can explain why miners may prioritize their own self-interest, even if it is not in the best interest of the network as a whole.

The first miner to solve a math problem gets fresh BTC units. Both computer power and energy usage are essential to the mining operation. Tragedy of the commons, which happens when individuals prioritize their own interests over the needs of the whole, is one of the biggest obstacles in cryptocurrency mining. By mining cryptocurrencies, miners may prioritize their individual financial gain above the network’s overall security and stability.

The prisoner’s dilemma provides a helpful foundation for understanding this behavior. In this scenario, two individuals are arrested for a crime and are given the option to work together or turn on each other. Their sentences are both lowered if they both cooperate. However, if one betrays the other, the betrayer receives a lighter punishment, while the other receives a lengthier one. They both receive moderate penalties if they betray each other.

Related: How does blockchain solve the Byzantine generals problem?

Miners encounter a similar decision-making process while mining cryptocurrencies. The network is safe and secure if all miners collaborate by mining honestly and making contributions. However, one miner may benefit more from mining maliciously or not contributing to the network if they prioritize their self-interest.

Below is a diagram illustrating an example of two miners in a cryptocurrency pool to comprehend how the prisoner’s dilemma can apply to the context of cryptocurrency mining.

The aforementioned diagram shows Miner A and Miner B are both miners in a cryptocurrency mining pool. They may choose to cooperate (mine together) or defect (leave the pool and mine independently). The rewards and payoffs are based on the classic prisoner’s dilemma scenario:

  • If both miners cooperate, they both receive a reward (e.g. a share of the mining profits).
  • If Miner A defects while Miner B cooperates, Miner A receives a temptation payoff (e.g. a larger share of the mining profits), while Miner B receives a suckers payoff (e.g. a smaller share of the mining profits).
  • If Miner A cooperates while Miner B defects, Miner A receives a suckers payoff, while Miner B receives a temptation payoff.
  • If both miners defect, they both receive a punishment (e.g. lower overall mining profits).

The above diagram illustrates how the prisoner’s dilemma can apply to the context of cryptocurrency mining. It shows the potential rewards and payoffs for each cooperation and defection combination, enabling miners to decide whether to stay in a pool or mine independently.

The defector obtains a larger share of profits because they are not sharing their earnings with the other miner. Conversely, the cooperator who remains in the pool will receive a smaller share of profits because they are contributing more computing power but receiving the same share of rewards as before.

To address this challenge, cryptocurrency networks can implement various incentives and mechanisms to incentivize miners to act in the interest of the network as a whole. For example, networks can reward miners who contribute to the network with lower fees or increased mining rewards. Furthermore, networks can implement penalties or defensive measures to prevent malicious behavior.

The game theory of blockchain forks

Blockchain forks are another situation where game theory can explain the decision-making process of participants. A fork emerges when a blockchain network splits into two separate paths, usually caused by disagreements among participants about the network’s direction.

Participants in a blockchain fork must work together in a coordination game to determine which fork to support and which to reject. The Bitcoin network divided into two distinct forks in 2017: Bitcoin and Bitcoin Cash. This is one of the most well-known instances of a blockchain fork. Disagreements within the Bitcoin community about how to expand the network to handle an increasing volume of transactions led to the creation of this fork.

In this scenario, members of the Bitcoin community were compelled to choose between sticking with the old Bitcoin network and switching to the new Bitcoin Cash network. The decision was difficult since each fork has its pros and cons. For example, while Bitcoin Cash offered faster transaction times and lower fees, Bitcoin had a larger network and more acceptance.

In light of game theory, participants in the aforementioned scenario must take their personal preferences and views concerning the potential future worth of each network into account. Participants may be motivated to promote Bitcoin Cash, even if it means leaving the original Bitcoin network if they believe it has a greater chance of long-term growth.

Related: How to buy Bitcoin Cash: A beginner’s guide for buying BCH

Below is a diagram showing two miners facing the choice of whether to adopt a new fork in the blockchain or stick with the old fork. It exemplifies how game theory can be applied to the context of blockchain forks.

The above diagram depicts Miner A and Miner B’s strategic decision-making on a blockchain as they face the choice of adopting a new fork or sticking with the old fork. The rewards and penalties are based on the following assumptions:

  • If both miners adopt the new fork, they both receive a reward (e.g. increased mining efficiency).
  • If Miner A adopts the new fork while Miner B continues on the old fork, Miner A receives a penalty (e.g. decreased mining efficiency), while Miner B receives a reward.
  • If Miner A continues on the old fork while Miner B adopts the new fork, Miner A receives a reward, while Miner B receives a penalty.
  • If both miners continue on the old fork, they both receive a temptation payoff (e.g. maintaining control over the blockchain).

The aforementioned diagram illustrates how game theory can apply to the context of blockchain forks. It shows the rewards and penalties for choosing to adopt or not adopt a new fork, and can help miners make decisions about whether to switch to a new fork or stick with the current one.

To address this challenge, cryptocurrency networks can implement various mechanisms to ensure that forks occur as smoothly as possible. For example, networks can implement replay protection to prevent transactions on one network from being replayed on the other.